Revision History for A053504
(Underlined text is an addition;
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Showing entries 1-10
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#27 by Charles R Greathouse IV at Thu Sep 08 08:45:00 EDT 2022
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| PROG
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(MAGMAMagma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^3/3 +x^4/4 +x^6/6 +x^8/8 +x^12/12 +x^24/24) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019
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Discussion
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| Thu Sep 08
| 08:45
| OEIS Server: https://oeis.org/edit/global/2944
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#26 by Bruno Berselli at Wed May 15 04:50:56 EDT 2019
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#25 by Michel Marcus at Wed May 15 04:27:16 EDT 2019
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#24 by G. C. Greubel at Wed May 15 03:15:45 EDT 2019
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#23 by G. C. Greubel at Wed May 15 03:15:37 EDT 2019
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| FORMULA
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E.g.f.: exp(x+1/2* + x^2+1/3*2 + x^3+1/4*3 + x^4+1/6*4 + x^6+1/8*6 + x^8+1/12*8 + x^12+1/24*12 + x^24/24).
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| MATHEMATICA
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a[n_] := _]:= a[n] = If[n<0, 0, If[n == ==0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 4, 6, 8, 12, 24}}]]]; Table[a[n], {n, 0, 2530}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)
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(PARI) N=2230; x='x+O('x^N);
(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^3/3 +x^4/4 +x^6/6 +x^8/8 +x^12/12 +x^24/24) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019
(Sage) m = 30; T = taylor(exp(x +x^2/2 +x^3/3 +x^4/4 +x^6/6 +x^8/8 +x^12/12 +x^24/24), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019
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approved
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#22 by Bruno Berselli at Thu May 11 10:28:39 EDT 2017
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#21 by Gheorghe Coserea at Thu May 11 09:33:21 EDT 2017
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#20 by Gheorghe Coserea at Thu May 11 09:32:05 EDT 2017
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(PARI) N=22; x='x+O('x^N);
Vec(serlaplace(exp(sumdiv(24, d, x^d/d)))) \\ Gheorghe Coserea, May 11 2017
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#19 by Harvey P. Dale at Sat Mar 05 09:19:23 EST 2016
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#18 by Harvey P. Dale at Sat Mar 05 09:19:16 EST 2016
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| MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[Total[x+x^2/2+x^3/3+x^4/4+ x^6/6+ x^8/8+ x^12/12+ x^24/^#/#&/@Divisors[24], {]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 05 2016 *)
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