A364376 G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^4).

1, 0, -1, 3, -4, -9, 73, -212, 111, 1956, -10078, 21466, 29823, -418183, 1561911, -1722963, -13205004, 86962328, -232448945, -109578204, 3849218852, -17135183489, 27800381006, 113891855632, -966644138742, 3075070731677, -833503324311, -41673632701038

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(n+3*k+1,k) * binomial(n+3*k+1,n-k) / (n+3*k+1).

G.f.: x/series_reversion(x*G(x)), where G(x) = 1 - x^2 + 3*x^3 - 6*x^4 + 6*x^5 + 15*x^6 - ... is the g.f. of A364372. - Peter Bala, Aug 27 2024

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+3*k+1, k)*binomial(n+3*k+1, n-k)/(n+3*k+1));

Crossrefs

Cf. A364372, A364374, A364375.

Cf. A215623.

Sequence in context: A015240 A032477 A073015 * A240546 A248003 A063930

Adjacent sequences: A364373 A364374 A364375 * A364377 A364378 A364379

Keyword

sign,easy

Author

Seiichi Manyama, Jul 21 2023

Status

approved