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%I #15 Nov 29 2022 01:21:05
%S 1,1,3,3,10,10,35,35,126,126,462,462,1716,1716,6435,6435,24310,24310,
%T 92378,92378,352716,352716,1352078,1352078,5200300,5200300,20058300,
%U 20058300,77558760,77558760,300540195,300540195
%N Binomial coefficients C(2n+1,n) repeated.
%C Hankel transform is A128017. Binomial transform is A005717(n+1).
%F G.f.: (1+x)*c(x^2)/sqrt(1-4x^2), c(x) the g.f. of A000108.
%F E.g.f.: exp(-x)*dif(exp(x)*Bessel_I(1,2x),x).
%F a(n) = C(n+1, n/2)*(1+(-1)^n)/2 + C(n, (n-1)/2)*(1-(-1)^n)/2; as moment sequence a(n) = (1/(2*Pi))*Integral_{x=-2..2} x^n*x*(1+x)/sqrt(4-x^2).
%F D-finite with recurrence: -(n+2)*(3*n-1)*a(n) - 4*a(n-1) + 4*n*(3*n+2)*a(n-2) = 0. - _R. J. Mathar_, Jun 17 2016
%F a(n) = A001700(floor(n/2)). - _Georg Fischer_, Nov 28 2022
%t With[{c=Table[Binomial[2n+1,n],{n,0,20}]},Riffle[c,c]] (* _Harvey P. Dale_, May 02 2012 *)
%Y Cf. A000108, A001700, A005717, A128017.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Feb 11 2007
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