A364864 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^3).

1, 1, 2, 4, 6, -1, -58, -304, -1090, -2876, -4216, 9244, 106746, 529962, 1874628, 4669760, 4309742, -35179252, -277928680, -1269921008, -4214431912, -9197175241, 30113526, 128659598896, 822227670866, 3453484223084, 10519017940952, 18490932535144

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(3*n+k+1,n) / (3*n+k+1).

a(n) = (1/n) * Sum_{k=0..n-1} (-2)^k * binomial(n,k) * binomial(4*n-k,n-1-k) for n > 0.

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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));

Crossrefs

Cf. A291534, A364865, A364866.

Cf. A002293, A336538.

Sequence in context: A004517 A254350 A357049 * A056649 A075242 A161489

Adjacent sequences: A364861 A364862 A364863 * A364865 A364866 A364867

Keyword

sign

Author

Seiichi Manyama, Aug 11 2023

Status

approved