A369478 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^2) ).

1, 4, 24, 170, 1320, 10868, 93197, 823484, 7445184, 68545882, 640446224, 6057249180, 57878746750, 557903174040, 5418441862824, 52971933934834, 520869559359424, 5147999004530720, 51113415228327827, 509583784051748692, 5099262428810825568

Offset: 0

Author

Seiichi Manyama, Jan 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A219537, A369480.

Cf. A143927, A369477.

Cf. A369441.

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)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(4*n-k+4,n-2*k).