A369481 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^3)) ).

1, 2, 5, 15, 51, 187, 718, 2844, 11530, 47612, 199576, 847013, 3632468, 15717041, 68527255, 300780438, 1327939406, 5893299392, 26275243626, 117635107818, 528631769323, 2383660351991, 10781500113896, 48903885040638, 222400899237943, 1013841791472632

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^3)))/x)
(PARI) a(n, s=3, t=1, 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. A071879, A369482.

Sequence in context: A124303 A367414 A073525 * A366096 A007317 A181768

Adjacent sequences: A369478 A369479 A369480 * A369482 A369483 A369484

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved