A365109 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^2.

1, 1, -2, 1, 6, -18, 8, 89, -266, 62, 1684, -4710, -220, 35648, -91236, -34871, 803302, -1856874, -1448844, 18809694, -38816620, -48910700, 451491680, -820626294, -1522994404, 11015923292, -17319046712, -45512957516, 271664145264, -359911736252, -1327355044924

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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=2) = 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, A365110, A365111, A365112.

Cf. A365085.

Sequence in context: A097947 A101032 A366356 * A025271 A153804 A239740

Adjacent sequences: A365106 A365107 A365108 * A365110 A365111 A365112

Keyword

sign

Author

Seiichi Manyama, Aug 22 2023

Status

approved