A357393 E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).

0, 1, 7, 110, 2730, 93024, 4037880, 213127200, 13253058000, 948964262400, 76899763100160, 6957624460550400, 695236239163065600, 76043127767523840000, 9036546669251861760000, 1159342449440429270016000, 159708538424128885551360000, 23512778013219939149561856000

Offset

0,3

Links

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

Formula

E.g.f. satisfies A(x) = log(1 + x * exp(4 * A(x))).

a(n) = Sum_{k=1..n} (3 * n)^(k-1) * |Stirling1(n,k)|.

a(n) = Sum_{k=1..n} (4 * n)^(k-1) * Stirling1(n,k).

a(n) = Product_{k=3*n+1..4*n-1} k = (4*n-1)!/(3*n)! for n > 0.

Prog

(PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*abs(stirling(n, k, 1)));
(PARI) a(n) = sum(k=1, n, (4*n)^(k-1)*stirling(n, k, 1));
(PARI) a(n) = if(n==0, 0, (4*n-1)!/(3*n)!);

Crossrefs

Cf. A006963, A357392.

Cf. A357334.

Sequence in context: A303109 A101924 A171193 * A371315 A212371 A112463

Adjacent sequences: A357390 A357391 A357392 * A357394 A357395 A357396

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2022

Status

approved