OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = binomial(n+4,4) - Sum_{k=0..n-5} a(k) * a(n-k-5).
G.f. A(x) satisfies: A(x) = 1/(1-x)^5 - x^5 * A(x)^2.
G.f.: 2 / ( (1-x)^2 * ((1-x)^3 + sqrt((1-x)^6 + 4*x^5*(1-x))) ).
PROG
(PARI) a(n) = sum(k=0, n\5, (-1)^k*binomial(n+4, 5*k+4)*binomial(2*k, k)/(k+1));
(PARI) my(N=40, x='x+O('x^N)); Vec(2/((1-x)^2*((1-x)^3+sqrt((1-x)^6+4*x^5*(1-x)))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 23 2023
STATUS
approved