A369477 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^2) ).

1, 3, 14, 77, 464, 2964, 19717, 135131, 947549, 6765642, 49022225, 359545750, 2664127354, 19913283809, 149968276974, 1136856855549, 8668000962927, 66428474900907, 511414514214628, 3953420853213504, 30674783555852576, 238808419235022293, 1864869207177530320

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^2)^2))/x)
(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

Crossrefs

Cf. A106228, A369479.

Cf. A143927, A369478.

Cf. A369440.

Sequence in context: A198656 A240402 A048779 * A052186 A330518 A228656

Adjacent sequences: A369474 A369475 A369476 * A369478 A369479 A369480

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved