A356882 E.g.f. satisfies: A(x) * log(A(x)) = x * (exp(x*A(x)) - 1).

1, 0, 2, 3, 16, 125, 756, 7567, 85968, 994905, 14373460, 225366251, 3800667960, 72169966453, 1469546796732, 32150706096615, 760806334538656, 19142440567996721, 512272692571487652, 14560087915617858883, 436598686303562722440, 13796641165956117509901

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A349560, A356785, A356788, A356789, A356883.

Cf. A349588.

Sequence in context: A067848 A269067 A370201 * A139802 A292207 A063666

Adjacent sequences: A356879 A356880 A356881 * A356883 A356884 A356885

Keyword

nonn

Author

Seiichi Manyama, Sep 02 2022

Status

approved