A368967 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^2)^2 ).

1, 4, 28, 238, 2244, 22568, 237199, 2574276, 28627224, 324503718, 3735672880, 43555658640, 513277420803, 6103767231712, 73153216133600, 882708243017414, 10714917867247020, 130752597362068496, 1603069096165788706, 19737123968746454284, 243930175282166574432

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..893
• Index entries for reversions of series

Crossrefs

Cf. A368961, A368965.

Cf. A368968.

Programs

PARI

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

PARI

a(n, s=2, t=2, 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(2*n+k+1,k) * binomial(5*n-k+3,n-2*k).