A365111 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^4.

1, 1, -4, 6, 16, -119, 240, 630, -5656, 13044, 31568, -323102, 816172, 1772553, -20373748, 55339784, 105991968, -1366239119, 3950894080, 6570520544, -95534073488, 292319792622, 414994066768, -6884779019086, 22198354364212, 26341578132594, -507524582140912

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

Prog

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

Crossrefs

Cf. A007440, A365109, A365110, A365112.

Cf. A365087.

Sequence in context: A264477 A223357 A083009 * A190968 A127416 A306017

Adjacent sequences: A365108 A365109 A365110 * A365112 A365113 A365114

Keyword

sign

Author

Seiichi Manyama, Aug 22 2023

Status

approved