A377438 E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^2.

1, 0, 4, 6, 136, 660, 13668, 128520, 2846240, 41368320, 1021615920, 20260896480, 564541372800, 14159468157120, 445236762450816, 13446791658256320, 474901138629918720, 16708336544212992000, 658279512232521209856, 26360704394322974161920, 1150065728368040063784960

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: 4/(1 + sqrt(1 + 4*x*log(1-x)))^2.

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371140.

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

Prog

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

Crossrefs

Cf. A052830, A377691.

Cf. A371140.

Sequence in context: A377688 A137025 A375689 * A355232 A377685 A176493

Adjacent sequences: A377434 A377435 A377436 * A377439 A377440 A377441

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2024

Status

approved