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#22 by Bruno Berselli at Thu Feb 02 03:43:37 EST 2017
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#21 by Joerg Arndt at Thu Feb 02 03:38:16 EST 2017
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#20 by Jon E. Schoenfield at Tue Jan 31 19:40:42 EST 2017
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#19 by Jon E. Schoenfield at Tue Jan 31 19:40:40 EST 2017
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| FORMULA
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G.f.: -3*(2333280*x^8 - - 5080464*x^7 + + 4500500*x^6 - - 2143640*x^5 + + 605675*x^4 - - 104636*x^3 + + 10850*x^2 - - 620*x + + 15) / ((x - - 1)*(2*x - - 1)*(3*x - - 1)*(4*x - - 1)*(5*x - - 1)*(6*x - - 1)*(7*x - - 1)*(8*x - - 1)*(9*x - - 1)). - Colin Barker, Jan 28 2015
a(n) = ) = (1/8!*!)*Sum_{k = 0..n} (-1)^(k+n)*(k + 10)!*Stirling2(n,k) /((k + 1)*(k + 2)). (End)
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| MAPLE
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seq(add(i*(10-i)^n, i = 1..9), n = 0..20); # - _); # _Peter Bala_, Jan 31 2017
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| STATUS
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proposed
editing
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#18 by Peter Bala at Tue Jan 31 13:00:48 EST 2017
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#17 by Peter Bala at Tue Jan 31 09:50:39 EST 2017
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| FORMULA
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For n >= 1, a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 01) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 01) )/(n + 2) at x = 9.
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Discussion
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| Tue Jan 31
| 13:00
| Peter Bala: Rearranged the formula for a(n) in Name section into a more natural form.
Note to self: Use 1/(x - 1)!*Sum_{k = 0..n} (-1)^(n+k)*Stirling2(n,k)*(x + k)!/(k + 1) = ( Bernoulli(n+1, x+1) - Bernoulli(n+1, 1) )/(n + 1) (see Wikipedia: Bernoulli polynomials - Relation to falling factorials) and Sum_{x = 1..N} (x + k)!/(x - 1)! = (N + k + 1)!/((N - 1)!(k + 2)).
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#16 by Peter Bala at Tue Jan 31 09:24:02 EST 2017
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| MAPLE
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seq(add(i*(10-i)^n, i = 1..9), n = 0..20); - _); # - _Peter Bala_, Jan 31 2017
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#15 by Peter Bala at Tue Jan 31 09:17:59 EST 2017
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| NAME
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a(n) = 8*2^n + 61*49^n + 2*8^n + 7*3*7^n + 4*6^n + 95*5^n + 56*54^n + 7*3^n + 8*72^n + 9*1^n.
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From Peter Bala, Jan 31 2016: (Start)
For n >= 1, a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 0) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 0) )/(n + 2) at x = 9.
a(n) = 1/8!*Sum_{k = 0..n} (-1)^(k+n)*(k + 10)!*Stirling2(n,k) /((k + 1)*(k + 2)). (End)
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| MAPLE
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seq(add(i*(10-i)^n, i = 1..9), n = 0..20); - Peter Bala, Jan 31 2017
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| STATUS
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approved
editing
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#14 by Charles R Greathouse IV at Sat Jun 13 00:55:22 EDT 2015
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| LINKS
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<a href="/index/Rec#order_09">Index to sequencesentries withfor linear recurrences with constant coefficients</a>, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).
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Discussion
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| Sat Jun 13
| 00:55
| OEIS Server: https://oeis.org/edit/global/2439
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#13 by Bruno Berselli at Wed Jan 28 06:11:43 EST 2015
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