A377376 Expansion of e.g.f. log( 1 - log(1 - x)^3 / 6 ).

0, 0, 0, 1, 6, 35, 215, 1414, 9912, 73324, 565170, 4472226, 35725426, 283350132, 2225790476, 18624038224, 216679183120, 4293834561200, 111300845967440, 2963219043255360, 76258914698507280, 1895550595605889760, 45928558583373219600, 1093984400513512753840

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=1..floor(n/3)} (-1)^(k-1) * (3*k)! * |Stirling1(n,3*k)|/(k * 6^k).

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

Prog

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

Crossrefs

Cf. A346966, A379674, A380370.

Sequence in context: A291246 A117671 A354136 * A370323 A317409 A354324

Adjacent sequences: A377373 A377374 A377375 * A377377 A377378 A377379

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2025

Status

approved