A369158 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^4) ).

1, 2, 5, 14, 43, 142, 495, 1794, 6686, 25436, 98311, 384826, 1522283, 6075838, 24437937, 98956270, 403080170, 1650502292, 6790018182, 28050896964, 116322826479, 484029536374, 2020386475025, 8457397801150, 35495812337114, 149336478356692, 629685490668799

Offset: 0

Author

Seiichi Manyama, Jan 15 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A127902, A369126, A369159.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^4))/x)

PARI

a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(2*n-2*k+2, n-4*k))/(n+1);

Formula

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