A365223 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^4).

1, 1, 2, 3, -3, -50, -244, -714, -530, 8522, 63548, 259473, 535647, -1321437, -19094684, -103022071, -322370363, -142186810, 5537336460, 41081448638, 170484444654, 332739198585, -1241023311708, -15677607031084, -83737193010368, -255608722098225, -12706843586158

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A000108, A106228, A127897, A364864.

Cf. A365224, A365226.

Sequence in context: A345751 A242786 A214219 * A323340 A280895 A088266

Adjacent sequences: A365220 A365221 A365222 * A365224 A365225 A365226

Keyword

sign

Author

Seiichi Manyama, Aug 27 2023

Status

approved