A369487 Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^2)^3 ).

1, 2, 10, 57, 365, 2492, 17797, 131290, 992704, 7652558, 59918667, 475213662, 3809620760, 30820493162, 251309225465, 2063207320841, 17040385542611, 141487339935740, 1180337222858348, 9888553030497869, 83160409524964381, 701782096849536054

Offset: 0

Author

Seiichi Manyama, Jan 24 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369488.

Programs

PARI

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

PARI

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

Formula

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