A317277 a(n) = Sum_{k=0..n} binomial(n-1,k-1)*k^n*n!/k!; a(0) = 1.
1, 1, 6, 81, 1828, 60565, 2734926, 160109005, 11724156648, 1045312448841, 111114793839610, 13845807451708441, 1994597720747571468, 328351264019737949341, 61162428777982281583302, 12782305566531823350524805, 2975150384583838798131401296, 766253903501365584725344992529
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
- N. J. A. Sloane, Transforms
Programs
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Magma
[1]cat[(&+[Binomial(n-1,j-1)*Binomial(n,j)*Factorial(n-j)*j^n: j in [0..n]]): n in [1..30]]; // G. C. Greubel, Mar 09 2021
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Maple
A317277:= n-> `if`(n=0,1, add(binomial(n-1,j-1)*binomial(n,j)*(n-j)!*j^n, j=0..n)); seq(A317277(n), n=0..30); # G. C. Greubel, Mar 09 2021
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Mathematica
Join[{1}, Table[Sum[Binomial[n - 1, k - 1] k^n n!/k!, {k, n}], {n, 17}]] Join[{1}, Table[n! SeriesCoefficient[Sum[k^n (x/(1 - x))^k/k!, {k, n}], {x, 0, n}], {n, 17}]] -
PARI
a(n) = if (n==0, 1, sum(k=0, n, binomial(n-1, k-1)*k^n*n!/k!)); \\ Michel Marcus, Mar 10 2021; corrected Jun 15 2022
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Sage
[1]+[sum(binomial(n-1,j-1)*binomial(n,j)*factorial(n-j)*j^n for j in (0..n)) for n in (1..30)] # G. C. Greubel, Mar 09 2021
Formula
a(n) = n! * [x^n] Sum_{k>=0} k^n*(x/(1 - x))^k/k!.
Extensions
Name edited by Michel Marcus, Jun 15 2022
Comments