OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/x*C(C(x)^2)/(C(x)*(1-x/(1-C(x))^2)), where C(x)=(1-sqrt(1-4*x))/2.
a(n) ~ 2^(2*n+1)/sqrt(Pi*n) * (1 - Gamma(3/4)/(sqrt(Pi)*n^(1/4)) + 7*sqrt(2*Pi) / (16*n^(3/4)*Gamma(3/4))). - Vaclav Kotesovec, Mar 18 2016
Conjecture: 3*n*(n-2)*(n+2)*a(n) -4*(n+1)*(8*n^2-23*n+12)*a(n-1) +16*n *(3*n-4)*(2*n-5)*a(n-2) +8*(2*n-3)*(4*n-7)*a(n-3) -64*(2*n-5)*(n-3)*(2*n-3)*a(n-4)=0. - R. J. Mathar, Jun 07 2016
MATHEMATICA
Table[Sum[Binomial[2*i+1, i]*Binomial[2*n-2*i, n]/(2*i+1), {i, 0, (n+1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 18 2016 *)
PROG
(Maxima) a(n):=sum(binomial(2*i+1, i)*binomial(2*n-2*i, n)/(2*i+1), i, 0, (n+1)/2);
(PARI) for(n=0, 25, print1(sum(k=0, n, binomial(2*k+1, k)*binomial(2*n-2*k, n)/(2*k+1)), ", ")) \\ G. C. Greubel, Jun 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 18 2016
STATUS
approved