OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..1110
FORMULA
a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+4*k-1,n-k).
n*a(n) = (10*n-8)*a(n-1) - (19*n-46)*a(n-2) + 20*(n-3)*a(n-3) - 15*(n-4)*a(n-4) + 6*(n-5)*a(n-5) - (n-6)*a(n-6) for n > 5.
a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (n+k) * binomial(n+3-k,4) * a(k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x)^5))
(PARI) a(n)=sum(k=0, n, binomial(2*k, k) * binomial(n+4*k-1, n-k)) \\ Winston de Greef, Mar 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 24 2023
STATUS
approved