OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..650
FORMULA
G.f.: (1+G003169(x))*G003169(x)/x, where G003169(x) is the g.f. of A003169.
Recurrence: 4*(n+1)*(2*n+1)*(17*n^2 - 28*n + 12)*a(n) = (1207*n^4 - 1988*n^3 + 1013*n^2 - 124*n - 12)*a(n-1) - 2*(n-2)*(2*n-3)*(17*n^2 + 6*n + 1)*a(n-2). - Vaclav Kotesovec, Jul 05 2014
a(n) ~ sqrt(95+393/sqrt(17)) * ((71+17*sqrt(17))/16)^n / (4*sqrt(2*Pi) * n^(3/2)). - Vaclav Kotesovec, Jul 05 2014
From Peter Bala, Sep 08 2024: (Start)
a(n) = (2/n) * Sum_{k = 0..n} binomial(n+1, n-k-1)*binomial(2*n, k)*2^(n-k) for n >= 1.
a(n) = 4*Jacobi_P(n-1, 2, n+1, 3)/n for n >= 1. Cf. A003168. (End)
PROG
(PARI) {a(n)=if(n==0, 1, sum(j=0, n, if(j==0, 1, sum(k=0, j, 2*binomial(j, k)*binomial(2*j+k, k-1)/j))* if(n-j==0, 1, sum(k=0, n-j, 2*binomial(n-j, k)*binomial(2*n-2*j+k, k-1)/(n-j)))))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna, Nov 17 2004
STATUS
approved