A372383 Expansion of (1/x) * Series_Reversion( x * (1+x)^3 / (1+x+x^2)^4 ).

1, 1, 5, 13, 63, 225, 1069, 4425, 21008, 93927, 449574, 2099993, 10161845, 48761421, 238544091, 1165258909, 5756929854, 28480358700, 141911407403, 708766944499, 3557401656125, 17900413391858, 90401732441880, 457657822713177, 2323507912981800, 11822283300379509

Offset: 0

Author

Seiichi Manyama, Apr 29 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A372382.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^3/(1+x+x^2)^4)/x)

PARI

a(n, s=2, t=4, u=-3) = 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(4*n+4,k) * binomial(n-k+1,n-2*k).