A386774 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1+2*x)^4 ).

1, 17, 439, 13513, 458196, 16518407, 621247194, 24099952473, 957294067516, 38741943503972, 1591753835634799, 66219447135668383, 2783826043226606236, 118078452737821009962, 5047034289902290964004, 217173909723115943823993, 9400092428228971114597356

Offset: 0

Author

Seiichi Manyama, Aug 02 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A386723, A386768, A386771.

Programs

PARI

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

PARI

a(n) = sum(k=0, n, 2^k*3^(n-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 * 3^(n-k) * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).

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