A377719 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^2.

1, 0, 4, 6, 128, 610, 12192, 112154, 2416416, 34337538, 827541200, 16047333082, 436958019984, 10718568174626, 329594991463584, 9737689680629850, 336439401299953472, 11581626068262440194, 446492838289046854320, 17496904148975860376474, 747070411957344952492080

Offset

0,3

Links

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

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371142.

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

Prog

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

Crossrefs

Cf. A371142, A377438.

Sequence in context: A337466 A052672 A375697 * A377688 A137025 A375689

Adjacent sequences: A377716 A377717 A377718 * A377720 A377721 A377722

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2024

Status

approved