A369400 Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3)^2 ).

1, 2, 5, 16, 62, 264, 1172, 5342, 24905, 118410, 572167, 2801354, 13865237, 69258500, 348698784, 1767724720, 9015710574, 46227736956, 238159867070, 1232206495528, 6399778252336, 33354634754364, 174390047681360, 914414985920664, 4807481173042396

Offset: 0

Author

Seiichi Manyama, Jan 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A396298.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^2*(1-x^3)^2)/x)

PARI

a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3)^2 )^(n+1). - Seiichi Manyama, Feb 16 2024