A356811 a(n) = Sum_{k=0..n} (k*n+1)^(n-k) * binomial(n,k).

1, 2, 8, 71, 1040, 22457, 676000, 26861977, 1347932416, 82873789793, 6114540967424, 532596023373713, 53990083205042176, 6289985311473281329, 833180470332123750400, 124356049859476364116193, 20754548375601491155681280, 3847574240184742568296430273

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..274

Formula

a(n) = n! * [x^n] exp( x * (exp(n * x) + 1) ).

a(n) = [x^n] Sum_{k>=0} x^k / (1 - (n*k+1)*x)^(k+1).

Prog

(PARI) a(n) = sum(k=0, n, (k*n+1)^(n-k)*binomial(n, k));

Crossrefs

Cf. A080108, A240165, A245834.

Cf. A356806, A356814, A356817.

Sequence in context: A330676 A062733 A180687 * A296629 A026739 A060635

Adjacent sequences: A356808 A356809 A356810 * A356812 A356813 A356814

Keyword

nonn

Author

Seiichi Manyama, Aug 29 2022

Status

approved