A293270 a(n) = n^n*binomial(2*n-1, n).

1, 1, 12, 270, 8960, 393750, 21555072, 1413199788, 107961384960, 9418192087590, 923780000000000, 100633991211229476, 12055263261877075968, 1575041416811693275900, 222887966509090352332800, 33962507149515380859375000, 5543988061027763016035205120

Offset: 0

Author

Ilya Gutkovskiy, Oct 04 2017

Keywords

• nonn

Comments

The n-th term of the n-fold convolution of the powers of n.

Crossrefs

Cf. A000312, A001700, A088218.

Cf. A001787, A027472, A036071, A036084, A036226, A038846, A053107, A053108, A053109.

Programs

Mathematica

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}]

PARI

a(n) = n^n*binomial(2*n-1, n); \\ Altug Alkan, Oct 04 2017

Formula

a(n) = [x^n] 1/(1 - n*x)^n.

a(n) ~ 2^(2*n-1)*n^n/sqrt(Pi*n).