A366023 Expansion of (1/x) * Series_Reversion( x*(1-x)*(1+x^4) ).

1, 1, 2, 5, 13, 36, 104, 309, 940, 2915, 9184, 29328, 94747, 309180, 1017824, 3376693, 11279274, 37906330, 128085630, 434913555, 1483226921, 5078436800, 17450556480, 60159492600, 208013078910, 721205983737, 2506764055592, 8733076109732, 30489081691750

Offset: 0

Author

Seiichi Manyama, Sep 26 2023

Keywords

• nonn

Crossrefs

Cf. A063019, A063026, A366024.

Programs

Mathematica

CoefficientList[InverseSeries[Series[x(1-x)(1+x^4),{x,0,29}],x]/x,x]  (* Stefano Spezia, Sep 26 2023 *)

PARI

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

Formula

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