A368965 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ).

1, 3, 17, 117, 895, 7309, 62410, 550431, 4975297, 45846977, 429095387, 4067760593, 38977419018, 376901628882, 3673226867356, 36043590216621, 355800292078095, 3530878133357175, 35205183620396571, 352505713454687599, 3543078943592291301

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..971
• Index entries for reversions of series

Crossrefs

Cf. A368961, A368967.

Cf. A368966.

Programs

PARI

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

PARI

a(n, s=2, t=2, 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(2*n+k+1,k) * binomial(4*n-k+2,n-2*k).