A369507 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).

1, 6, 51, 508, 5535, 63888, 767689, 9502254, 120324606, 1551362160, 20296839585, 268785905790, 3595951246855, 48528885742200, 659856371680971, 9031161933443468, 124319953470044970, 1720113658097639532, 23908612149570793386, 333680424238179500976

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369483, A369504.

Programs

PARI

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

PARI

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

Formula

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