A397321 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^4) - 1)) ).

1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 21772800, 0, 0, 1037836800, 697426329600, 66691392768000, 0, 14820309504000, 37347179950080000, 14050009097220096000, 1231048416137379840000, 425757851430912000, 3372002183332823040000, 3500793933390673920000000

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 * (exp((x * A(x))^4) - 1).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (2*n-4*k)! * Stirling2(k,n-4*k)/k!.

Prog

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

Crossrefs

Cf. A370988, A376345, A376347.

Cf. A392790, A397281.

Sequence in context: A243779 A267335 A357968 * A397322 A392796 A392793

Adjacent sequences: A397317 A397319 A397320 * A397322 A397323 A397324

Keyword

nonn,new

Author

Seiichi Manyama, Jun 21 2026

Status

approved