OFFSET
0,2
FORMULA
G.f.: A(x) = 2*(1+x)/((1+2*x + G(x))*G(x)) where G(x) = sqrt(1 - 4*x*(1+x)^2).
a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n-k+2*j,j)*C(n-k+2*j,k-j).
D-finite with recurrence 2*(n+1)*a(n) +(-3*n-7)*a(n-1) +2*(-17*n+10)*a(n-2) +8*(-7*n+10)*a(n-3) +2*(-18*n+37)*a(n-4) +4*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Jun 23 2023
PROG
(PARI) {a(n)=sum(k=0, n, sum(j=0, k, binomial(2*j+n-k, j)*binomial(2*j+n-k, k-j)))} /* Using the g.f.: */ {a(n)=local(G=sqrt(1 - 4*x*(1+x)^2 +x*O(x^n))); polcoeff(2*(1+x)/((1+2*x+G)*G), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2008
STATUS
approved