A377445 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^2.

1, 2, 16, 226, 4678, 128728, 4437416, 184176816, 8949477600, 498611374704, 31343763192144, 2194986671431200, 169478318264408832, 14304849733469090976, 1310439414650613267552, 129495512412669053694720, 13731040497246647099309568, 1555129289690056322821075968

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367158.

a(n) = 2 * Sum_{k=0..n} (3*k+1)!/(2*k+2)! * |Stirling1(n,k)|.

a(n) ~ 27 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - Vaclav Kotesovec, Aug 27 2025

Mathematica

Table[2*Sum[(3*k+1)!/(2*k+2)! * Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 27 2025 *)

Prog

(PARI) a(n) = 2*sum(k=0, n, (3*k+1)!/(2*k+2)!*abs(stirling(n, k, 1)));

Crossrefs

Cf. A052803, A377446, A377449.

Cf. A367158.

Sequence in context: A047657 A377452 A233141 * A223631 A188500 A188515

Adjacent sequences: A377442 A377443 A377444 * A377446 A377447 A377448

Keyword

nonn

Author

Seiichi Manyama, Oct 28 2024

Status

approved