A369512 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x)^2 ).

1, 8, 106, 1706, 30459, 580138, 11548831, 237408978, 5001034821, 107387829120, 2341915361920, 51727723741200, 1154821390130868, 26016595619565008, 590718564607726952, 13504019611821648448, 310553715057038411358, 7179645587769992602252

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369215.

Programs

Mathematica

CoefficientList[InverseSeries[Series[x((1-x)^3-x)^2,{x,0,18}],x]/x,x] (* Stefano Spezia, Mar 31 2025 *)

PARI

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

PARI

a(n) = sum(k=0, n, binomial(2*n+k+1, k)*binomial(7*n+2*k+5, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(7*n+2*k+5,n-k).