A369441 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^2)^2) ).

1, 2, 7, 30, 141, 704, 3666, 19686, 108222, 606062, 3445308, 19829680, 115323955, 676659960, 4000719012, 23811922678, 142557391306, 857894530348, 5186614665121, 31487226410770, 191871141682557, 1173163962971056, 7195329233469552, 44255915928488880

Offset: 0

Author

Seiichi Manyama, Jan 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369440.

Programs

PARI

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

PARI

a(n, s=2, t=2, 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(2*n+2,k) * binomial(2*n+2,n-2*k).