login
A137637
a(n) = Sum_{k=0..n} C(2k+2,k)*C(2k+2,n-k) ; equals row 2 of square array A137634 ; also equals the convolution of A137635 and the self-convolution of A073157.
5
1, 6, 32, 170, 899, 4764, 25318, 134964, 721562, 3868024, 20785035, 111931154, 603938905, 3264309644, 17671408012, 95800342628, 520022296700, 2826089180652, 15374990077568, 83727902852188, 456370687687082
OFFSET
0,2
LINKS
FORMULA
G.f.: A(x) = R(x)*G(x)^2, where R(x) = 1/sqrt(1-4*x*(1+x)^2) is the g.f. of A137635 and G(x) = (1-sqrt(1-4*x*(1+x)^2))/(2*x*(1+x)) is the g.f. of A073157.
PROG
(PARI) {a(n)=sum(k=0, n, binomial(2*k+2, k)*binomial(2*k+2, n-k))} /* Using the g.f.: */ {a(n)=local(R=1/sqrt(1-4*x*(1+x +x*O(x^n))^2), G=(1-sqrt(1-4*x*(1+x)^2+x^2*O(x^n)))/(2*x*(1+x+x*O(x^n)))); polcoeff(R*G^2, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2008
STATUS
approved