A377581 E.g.f. satisfies A(x) = 1 + x * exp(x*A(x)^4).

1, 1, 2, 27, 340, 6485, 156486, 4532647, 155359016, 6116223465, 272369488330, 13537882005131, 742838308204092, 44605728508797469, 2909444391161677838, 204844046364505460655, 15484082153045052133456, 1250714994867101307618257, 107511883999692161772696210

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A161631, A364978, A364979.

Cf. A377579, A377580.

Sequence in context: A091709 A083384 A121971 * A278790 A277832 A221674

Adjacent sequences: A377578 A377579 A377580 * A377582 A377583 A377584

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2024

Status

approved