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))) ).
D-finite with recurrence (n+5)*a(n) +6*(-n-4)*a(n-1) +15*(n+3)*a(n-2) +20*(-n-2)*a(n-3) +15*(n+1)*a(n-4) +10*(-n+1)*a(n-5) +5*(n-1)*a(n-6)=0. - R. J. Mathar, Jan 25 2023
PROG
(PARI) a(n) = sum(k=0, n\5, 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
nonn
AUTHOR
Seiichi Manyama, Jan 23 2023
STATUS
approved