A371023 E.g.f. satisfies log(A(x)) = x*A(x)^2 * (exp(x*A(x)^2) - 1).

1, 0, 2, 3, 112, 665, 23016, 292957, 10710960, 223877313, 9010822600, 266949248621, 12012620436312, 461111201730049, 23286625765980864, 1093225826724243045, 61822510319788946656, 3415325919719802626177, 215162865022831595415576

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

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

Crossrefs

Cf. A356785, A356788, A356797.

Sequence in context: A114373 A117700 A356789 * A084755 A215238 A374873

Adjacent sequences: A371020 A371021 A371022 * A371024 A371025 A371026

Keyword

nonn

Author

Seiichi Manyama, Mar 12 2024

Status

approved