A384202 Expansion of e.g.f. -log(1 - 3*x)/(3 * (1 + x)).

0, 1, 1, 15, 102, 1434, 20556, 380988, 7974576, 192768336, 5214883680, 156913290720, 5188181880960, 187114724853120, 7308276334974720, 307346919257952000, 13846147184588544000, 665272996712352000000, 33958618500545883648000, 1835197000323512071680000

Offset

0,4

Links

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

Formula

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

a(n) = -n * a(n-1) + 3^(n-1) * (n-1)!.

a(n) = (2*n-3) * a(n-1) + 3 * (n-1)^2 * a(n-2).

Prog

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

Crossrefs

Cf. A384201.

Sequence in context: A383665 A085465 A205424 * A219624 A219170 A227331

Adjacent sequences: A384199 A384200 A384201 * A384203 A384204 A384205

Keyword

nonn,easy

Author

Seiichi Manyama, May 22 2025

Status

approved