A377746 E.g.f. satisfies A(x) = exp(x) * (1 + x * A(x)^2)^2.

1, 3, 31, 637, 19813, 830671, 43938067, 2809979257, 210946285417, 18189526062331, 1771938448807591, 192475338784416469, 23068103047077997069, 3023954831626697490055, 430420617664714578381019, 66110112671342637934719121, 10898800684623601950111879505, 1919585083312849130822156455795

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

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

Crossrefs

Cf. A377740.

Sequence in context: A222895 A373754 A105293 * A368489 A380513 A104841

Adjacent sequences: A377743 A377744 A377745 * A377747 A377748 A377749

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2024

Status

approved