OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..941
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n-1,n-k).
D-finite with recurrence 96*(3*n+2)*(3*n+1)*(n+1)*a(n) +4*(-4121*n^3 +1922*n^2 -1273*n+124)*a(n-1) +4*(20588*n^3 -76648*n^2 +98677*n -43586)*a(n-2) +(-90073*n^3 +671565*n^2 -1665278*n +1375320)*a(n-3) +210*(n-4)*(3*n-7) *(3*n-8)*a(n-4)=0. - R. J. Mathar, Jan 25 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x/(1-x))^3)/x)
(PARI) a(n, s=1, t=3, u=-3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 11 2024
STATUS
approved