A369504 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^3)^2 ).

1, 4, 22, 142, 1005, 7546, 59033, 475962, 3927204, 33001024, 281449964, 2429922400, 21196031340, 186521336460, 1653830553417, 14761130834428, 132516050272100, 1195778542160992, 10839917478886459, 98671228898404032, 901509955793840923

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369502, A369503.

Cf. A369212.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(4*n-2*k+4,n-3*k).