A377687 E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^3).

1, 0, 2, 3, 80, 570, 12744, 198660, 4969152, 119968128, 3607836480, 115031711520, 4163170478400, 162622297300320, 6952158785424384, 319741032356928000, 15818989359665802240, 835755271882288128000, 47015148988105365288960, 2804276310235518168161280

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (3*n-3*k)! * |Stirling1(n-k,k)|/( (n-k)! * (3*n-4*k+1)! ).

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (3*n-3*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(3*n-4*k+1)!));

Crossrefs

Cf. A371227, A377690.

Sequence in context: A371141 A370993 A371228 * A068185 A037391 A037427

Adjacent sequences: A377684 A377685 A377686 * A377688 A377689 A377690

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2024

Status

approved