A369159 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^4) ).

1, 3, 12, 55, 274, 1443, 7905, 44593, 257305, 1511553, 9010170, 54361486, 331336454, 2037132958, 12619056108, 78682008194, 493427982703, 3110202012353, 19693920616872, 125214061831251, 799059649687239, 5116372686471627, 32860439054510610

Offset: 0

Author

Seiichi Manyama, Jan 15 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A127902, A369126, A369158.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^4))/x)

PARI

a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(3*n-3*k+3, n-4*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(3*n-3*k+3,n-4*k).