A369439 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^2)) ).

1, 2, 6, 22, 89, 382, 1708, 7870, 37108, 178184, 868318, 4283402, 21347902, 107330004, 543707480, 2772469998, 14219396908, 73303128344, 379621891640, 1974078923416, 10303600000553, 53960438323438, 283461807342876, 1493252678987602, 7886649917261724

Offset: 0

Author

Seiichi Manyama, Jan 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A036765.

Programs

PARI

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

PARI

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

Formula

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