A119359 Central coefficients of number triangle A119326.

0, 1, 1, 7, 31, 106, 386, 1499, 5755, 21886, 83854, 323302, 1248534, 4828916, 18719364, 72711123, 282867795, 1101981430, 4298723990, 16788997874, 65641296578, 256895812108, 1006307847324, 3945185527582, 15478851119966

Offset

0,4

Comments

a(n) = A119326(2n,n+1). A119358(n)-a(n) = A071688(n).

Links

Table of n, a(n) for n=0..24.

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

Sequence in context: A107392 A054497 A235593 * A055366 A160607 A205492

Adjacent sequences: A119356 A119357 A119358 * A119360 A119361 A119362

Keyword

easy,nonn

Author

Paul Barry, May 16 2006

Status

approved