A377580 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)^2))^2.

1, 2, 6, 66, 920, 17450, 425772, 12443438, 428469456, 16947065682, 757343738900, 37752522755222, 2076633137032632, 124956870908294906, 8165077881669520476, 575775223046122068510, 43582446983541508540832, 3524622951250814296207010, 303306411871327203664657956

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377581.

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

Prog

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

Crossrefs

Cf. A377579, A377581.

Sequence in context: A082619 A046399 A082617 * A006517 A395842 A217630

Adjacent sequences: A377577 A377578 A377579 * A377581 A377582 A377583

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2024

Status

approved