A397322 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^4)) ).

1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 21772800, 0, 0, 2075673600, 697426329600, 66691392768000, 0, 88921857024000, 58688425635840000, 14050009097220096000, 1231048416137379840000, 10218188434341888000, 11240007277776076800000, 4901111506746943488000000

Offset

0,6

Links

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

Formula

E.g.f. A(x) satisfies A(x) = 1 - x * A(x)^2 * log(1 - (x * A(x))^4).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (2*n-4*k)! * |Stirling1(k,n-4*k)|/k!.

Prog

(PARI) a(n) = sum(k=0, n\4, (2*n-4*k)!*abs(stirling(k, n-4*k, 1))/k!)/(n+1);

Crossrefs

Cf. A370993, A376344, A376346.

Cf. A392785, A397283.

Sequence in context: A267335 A357968 A397321 * A392796 A392793 A156415

Adjacent sequences: A397319 A397320 A397321 * A397323 A397324 A397325

Keyword

nonn

Author

Seiichi Manyama, Jun 21 2026

Status

approved