A386723 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1+2*x)^4 ).

1, 11, 175, 3275, 67156, 1460237, 33073930, 771961835, 18437940220, 448483875596, 11071403236807, 276675755470349, 6985664542196380, 177932236341440270, 4566561255466298500, 117974930924420353835, 3065563791639454312492, 80069021664742889373380

Offset: 0

Author

Seiichi Manyama, Jul 31 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371391, A386722.

Cf. A386719.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1+2*x)^4)/x)

PARI

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

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^4 / (1-x)^3 )^(n+1).