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A293270
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a(n) = n^n*binomial(2*n-1, n).
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1
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1, 1, 12, 270, 8960, 393750, 21555072, 1413199788, 107961384960, 9418192087590, 923780000000000, 100633991211229476, 12055263261877075968, 1575041416811693275900, 222887966509090352332800, 33962507149515380859375000, 5543988061027763016035205120
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OFFSET
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0,3
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COMMENTS
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The n-th term of the n-fold convolution of the powers of n.
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LINKS
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FORMULA
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a(n) = [x^n] 1/(1 - n*x)^n.
a(n) ~ 2^(2*n-1)*n^n/sqrt(Pi*n).
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MATHEMATICA
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Join[{1}, Table[n^n Binomial[2 n - 1, n], {n, 1, 16}]]
Join[{1}, Table[(-1)^n n^n Binomial[-n, n], {n, 1, 16}]]
Table[SeriesCoefficient[1/(1 - n x)^n, {x, 0, n}], {n, 0, 16}]
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PROG
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(PARI) a(n) = n^n*binomial(2*n-1, n); \\ Altug Alkan, Oct 04 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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