A367427 Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(3/4).

1, 3, 33, 579, 13857, 419427, 15344769, 658225635, 32388324801, 1798082759235, 111173908726881, 7575821838083331, 564099365435411169, 45567223702943324067, 3968829692958916703169, 370764641464637535547299, 36980399763333881818665345

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+3)) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} 4^k * (1 - 1/4 * k/n) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, 4^(n-k)*prod(j=0, k-1, 4*j+3)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A367429.

Sequence in context: A083080 A002916 A009659 * A361212 A144756 A377453

Adjacent sequences: A367424 A367425 A367426 * A367428 A367429 A367430

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2023

Status

approved