OFFSET
0,4
FORMULA
G.f.: (1/sqrt(1-4x)+(1/sqrt(1+4x^2)-1)-c(x)+x*c(-x^2))/2, c(x) the g.f. of A000108;
a(n) = (C(2n,n+1)+C((n-1)/2)*sin(Pi*n/2)-2*0^n-2C(n-1,n/2)*sin(Pi*(n-1)/2))/2.
a(n) = hypergeom([-1/2-n/2, 1/2-n/2, 1-n/2, -n/2], [1/2, 1/2, 1], 1) - 0^n. - Vladimir Reshetnikov, Oct 04 2016
MATHEMATICA
Table[HypergeometricPFQ[{-1/2 - n/2, 1/2 - n/2, 1 - n/2, -n/2}, {1/2, 1/2, 1}, 1] - KroneckerDelta[n], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 04 2016 *)
Table[(2^n Binomial[1/2, (n+1)/2] + Binomial[n, n/2] Cos[Pi n/2] + n CatalanNumber[n])/2 - KroneckerDelta[n], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 06 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2006
STATUS
approved