A369506 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^2)^2 ).

1, 6, 53, 548, 6192, 74074, 922142, 11822082, 155024190, 2069570934, 28033435791, 384329462490, 5322745393480, 74357950874850, 1046564375245893, 14826433687124098, 211251475010201934, 3025331234242178508, 43523061969049245589, 628692982662691174722

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A143927, A369503.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-2*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-2*k).