A369215 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x) ).

1, 4, 29, 261, 2627, 28315, 319648, 3731037, 44663058, 545312504, 6764556591, 85015779095, 1080185111768, 13852183882612, 179058158369828, 2330621446075640, 30519758687849439, 401806204894374041, 5315243189757111099, 70613088335938995385, 941714812929017751855

Offset: 0

Author

Seiichi Manyama, Jan 16 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..868
• Index entries for reversions of series

Crossrefs

Cf. A369114, A369161.

Cf. A151374, A249924, A369216.

Cf. A365764, A379171, A379172.

Cf. A049140.

Programs

Mathematica

CoefficientList[InverseSeries[Series[x((1-x)^3-x),{x,0,21}],x]/x,x] (* Stefano Spezia, Mar 31 2025 *)

PARI

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

PARI

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

Formula

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