A369488 Expansion of (1/x) * Series_Reversion( x / (1-x)^2 * (1-x-x^2)^3 ).

1, 1, 5, 20, 101, 522, 2860, 16115, 93200, 549286, 3288633, 19942666, 122243210, 756188245, 4714629930, 29595888020, 186903732003, 1186606564605, 7569137651545, 48486925091800, 311788811682494, 2011863788481296, 13022795014568290, 84539592912435990

Offset: 0

Author

Seiichi Manyama, Jan 24 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369487.

Programs

PARI

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

PARI

a(n, s=2, t=3, u=2) = 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(2*n-k,n-2*k).