A369300 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^3 ).

1, 2, 7, 33, 173, 962, 5589, 33546, 206359, 1294096, 8242375, 53173095, 346724250, 2281555440, 15131448440, 101038950441, 678724811604, 4583483218340, 31098830566098, 211898222878937, 1449322361547669, 9947227335902244, 68486384818253877

Offset: 0

Author

Seiichi Manyama, Jan 18 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A369299, A369301.

Cf. A369297, A369298.

Cf. A369269.

Programs

PARI

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

PARI

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

Formula

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

a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024