A366112 Expansion of (1/x) * Series_Reversion( x*(1-x-x^5)/(1-x) ).

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 7, 14, 22, 31, 41, 103, 235, 457, 791, 1261, 2399, 5015, 10257, 19676, 35296, 65170, 127520, 256187, 507601, 969495, 1834433, 3534477, 6962249, 13809538, 27061252, 52439361, 101701035, 199152071, 393332277, 776589611, 1525416837

Offset: 0

Author

Seiichi Manyama, Sep 29 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A046736, A054514, A215342.

Cf. A017899.

Programs

Mathematica

CoefficientList[InverseSeries[Series[x*(1-x-x^5)/(1-x),{x,0,41}]]/x,x] (* Stefano Spezia, Aug 21 2025 *)

PARI

a(n) = sum(k=0, n\5, binomial(n+k, k)*binomial(n-4*k-1, n-5*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} binomial(n+k,k) * binomial(n-4*k-1,n-5*k).