A362862 a(n) = (-1)^n * Sum_{k=0..n} (-n*k)^k * binomial(n,k).

1, 0, 13, 629, 58993, 8998399, 2035844461, 640881617123, 267995012680641, 143734541641235567, 96200314049944377901, 78599287990433271805699, 76993408916168689318057201, 89072357257840197226050646151

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

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

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

Prog

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

Crossrefs

Main diagonal of A362019.

Cf. A290158.

Sequence in context: A296951 A374605 A372243 * A351507 A067407 A143734

Adjacent sequences: A362859 A362860 A362861 * A362863 A362864 A362865

Keyword

nonn

Author

Seiichi Manyama, May 06 2023

Status

approved