OFFSET
0,3
FORMULA
G.f. satisfies A(x) = 1 + x*A(x)^2*(1 + x^4*A(x)^3).
a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k,k) * binomial(2*n-5*k+1,n-4*k)/(2*n-5*k+1) = (1/(n+1)) * Sum_{k=0..floor(n/5)} binomial(n+1,k) * binomial(2*n-5*k,n-5*k).
MATHEMATICA
CoefficientList[InverseSeries[Series[x(1-x)/(1+x^5), {x, 0, 28}], x]/x, x] (* Stefano Spezia, Sep 26 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(2*n-5*k+1, n-4*k)/(2*n-5*k+1));
(PARI) Vec(serreverse(x*(1-x)/(1+x^5)+O(x^30))/x) \\ Michel Marcus, Sep 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 26 2023
STATUS
approved