OFFSET
0,2
FORMULA
a(n) = binomial(n+4,4) + Sum_{k=0..n-1} a(k) * a(n-k-1).
G.f. A(x) satisfies A(x) = 1/(1-x)^5 + x * A(x)^2.
G.f.: 2 / ( (1-x)^5 * (1 + sqrt( 1 - 4*x/(1-x)^5 )) ).
D-finite with recurrence (n+1)*a(n) +2*(-5*n+1)*a(n-1) +(19*n-11)*a(n-2) +20*(-n+2)*a(n-3) +15*(n-3)*a(n-4) +6*(-n+4)*a(n-5) +(n-5)*a(n-6)=0. - R. J. Mathar, Jan 25 2023
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+4*k+4, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(2/((1-x)^5*(1+sqrt(1-4*x/(1-x)^5))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 23 2023
STATUS
approved