A368174 Expansion of e.g.f. -log(1 - x^3/6 * (exp(x) - 1)).

0, 0, 0, 0, 4, 10, 20, 35, 616, 5124, 29520, 138765, 1312300, 16576846, 175795984, 1539037955, 15687832720, 216382727240, 3170822906976, 42007311638169, 553841577209940, 8435274815148370, 145708900713412960, 2517047758252082671, 42575155321545439384

Offset: 0

Author

Seiichi Manyama, Dec 14 2023

Keywords

• nonn

Comments

This sequence is different from A354001.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..471

Crossrefs

Cf. A052858, A368173.

Cf. A353999, A354001.

Programs

PARI

a(n) = n!*sum(k=1, n\4, (k-1)!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).

a(0) = a(1) = a(2) = a(3) = 0; a(n) = binomial(n,3) + Sum_{k=4..n-1} binomial(k,3) * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025