A356817 a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).

1, -2, 0, 1, 144, 4143, 110368, 2535475, 13299968, -5169863825, -639341093376, -59073970497885, -4677854594527232, -276406098219258425, 2399871442122924032, 5163244810691492730907, 1331213942683118587674624, 262517264591996332314037215

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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, (-1)^k*(k*n-1)^(n-k)*binomial(n, k));

Crossrefs

Cf. A356815, A356816, A356818.

Cf. A356806, A356811, A356814.

Sequence in context: A158234 A270882 A278778 * A285931 A069845 A091397

Adjacent sequences: A356814 A356815 A356816 * A356818 A356819 A356820

Keyword

sign

Author

Seiichi Manyama, Aug 29 2022

Status

approved