A368964 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3)^3 ).

1, 3, 15, 94, 660, 4959, 38995, 316875, 2639754, 22423292, 193484208, 1691190228, 14942632450, 133242614565, 1197520200870, 10836727044255, 98656011543816, 902936341411170, 8303218554134769, 76679352910367832, 710839322080978272, 6612557820697157410

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(4*n-2*k+2,n-3*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A368963, A368972.

Sequence in context: A128240 A369270 A369301 * A274734 A177341 A220262

Adjacent sequences: A368961 A368962 A368963 * A368965 A368966 A368967

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved