A367428 Expansion of e.g.f. 1 / (1 - log(1 + 3*x))^(2/3).

1, 2, 4, 26, 106, 1508, 5860, 221240, -105080, 68914880, -673608800, 40800296480, -879775393760, 40553067851840, -1318206835981760, 60190275180475520, -2497504364769226880, 122572211951306635520, -6006028623693488806400, 324246374847303660704000

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * (Product_{j=0..k-1} (3*j+2)) * Stirling1(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-3)^k * (1/3 * k/n - 1) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+2)*stirling(n, k, 1));

Crossrefs

Cf. A352070, A365599.

Sequence in context: A155120 A356442 A144691 * A085700 A087404 A009237

Adjacent sequences: A367425 A367426 A367427 * A367429 A367430 A367431

Keyword

sign

Author

Seiichi Manyama, Nov 18 2023

Status

approved