A377688 E.g.f. satisfies A(x) = (1 + x * (exp(x*A(x)) - 1))^2.

1, 0, 4, 6, 128, 850, 13872, 195314, 3586592, 74163618, 1694735840, 44196946882, 1244904944208, 38788984768274, 1302631536943856, 47297768099973330, 1840951270666885952, 76501162074673415746, 3382517582789739956928, 158445187728836733069986

Offset

0,3

Links

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371262.

a(n) = 2 * n! * Sum_{k=0..floor(n/2)} (2*n-2*k+1)! * Stirling2(n-k,k)/( (n-k)! * (2*n-3*k+2)! ).

Prog

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

Crossrefs

Cf. A371115, A377689.

Cf. A371262.

Sequence in context: A052672 A375697 A377719 * A137025 A375689 A377438

Adjacent sequences: A377685 A377686 A377687 * A377689 A377690 A377691

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2024

Status

approved