Revision History for A054592
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#20 by Michael De Vlieger at Fri Feb 24 16:27:57 EST 2023
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#19 by Peter Luschny at Fri Feb 24 15:58:03 EST 2023
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#18 by Peter Luschny at Fri Feb 24 15:57:26 EST 2023
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| FORMULA
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a(n) = n) = [!*[x^n] (](g - log(g) - 1) where g = Sum_{n>=0} 2^binomial(n, 2) * x^n / n!. - Geoffrey Critzer, Nov 11 2011
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| EXTENSIONS
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ExtendedEdited and extended with a(0) = 0 by Peter Luschny, Feb 24 2023
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#17 by Peter Luschny at Fri Feb 24 15:51:10 EST 2023
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| FORMULA
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a(n) = [x^n] (g - log(g) - 1) where g = Sum_{n>=0} 2^binomial(n, 2) * x^n / n!. - Geoffrey Critzer, Nov 11 2011
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Discussion
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| Fri Feb 24
| 15:55
| Peter Luschny: Critzer's transform series formula extracted to the formula section.
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#16 by Peter Luschny at Fri Feb 24 15:47:13 EST 2023
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| DATA
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0, 0, 1, 4, 26, 296, 6064, 230896, 16886864, 2423185664, 687883494016, 387139470010624, 432380088071584256, 959252253993204724736, 4231267540316814507357184, 37138269572860613284747227136, 649037449132671895468073434916864, 22596879313063804832510513481261154304
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| MAPLE
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upto := 18: g := add(2^binomial(n, 2) * x^n / n!, n = 0..upto+1):
ser := series(g - log(g) - 1, x, upto+1):
seq(n!*coeff(ser, x, n), n = 0..upto); # Peter Luschny, Feb 24 2023
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#15 by Peter Luschny at Fri Feb 24 15:36:21 EST 2023
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#14 by Peter Luschny at Fri Feb 24 15:35:56 EST 2023
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#13 by Peter Luschny at Fri Feb 24 15:31:30 EST 2023
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| DATA
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0, 0, 1, 4, 26, 296, 6064, 230896, 16886864, 2423185664, 687883494016, 387139470010624, 432380088071584256, 959252253993204724736, 4231267540316814507357184, 37138269572860613284747227136
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| OFFSET
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1,34
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| EXTENSIONS
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Extended with a(0) = 0 by Peter Luschny, Feb 24 2023
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#12 by Peter Luschny at Fri Feb 24 15:29:30 EST 2023
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| COMMENTS
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a(n)=2^binomial(n,2)-A001187(n)
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| FORMULA
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a(n) = 2^binomial(n, 2) - A001187(n).
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| STATUS
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approved
editing
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#11 by Charles R Greathouse IV at Sun Aug 03 14:29:46 EDT 2014
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| MATHEMATICA
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g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}]; Range[0, 20]! CoefficientList[Series[g-Log[g]-1, {x, 0, 20}], x] (* ] (* _Geoffrey Critzer, _, Nov 11 2011 *)
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Discussion
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| Sun Aug 03
| 14:29
| OEIS Server: https://oeis.org/edit/global/2274
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