A369630 Expansion of (1/x) * Series_Reversion( x * (1/(1+x^3) - x) ).

1, 1, 2, 6, 20, 70, 255, 960, 3707, 14598, 58395, 236626, 969275, 4007041, 16696822, 70053159, 295691622, 1254772103, 5349978803, 22907982780, 98466168572, 424713570017, 1837717336614, 7974744620620, 34698200181696, 151341512079231, 661590732178716

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x^3)-x))/x)
(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k+1, k)*binomial(2*n-3*k, n-3*k))/(n+1);

Crossrefs

Cf. A007863, A199874, A369631.

Cf. A226974.

Sequence in context: A078482 A049128 A192540 * A185202 A340891 A049140

Adjacent sequences: A369627 A369628 A369629 * A369631 A369632 A369633

Keyword

nonn

Author

Seiichi Manyama, Jan 28 2024

Status

approved