A026163 Sum{T(k,k-1)}, k = 1,2,...,n, where T is the array in A026148.

1, 2, 6, 16, 45, 126, 356, 1008, 2862, 8140, 23188, 66144, 188916, 540216, 1546560, 4432512, 12717513, 36526626, 105016686, 302228080, 870613689, 2510249302, 7244285436, 20924179920, 60487084775, 174994990326, 506669921982

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

Conjectures from Mark van Hoeij, Oct 30 2011: (Start)

a(n) = -4*(-3)^(1/2)*(-1)^n*((n^3+11*n^2+48*n+45)*hypergeom([1/2, n+2],[1],4/3)+(3*n^2+11*n+15)*hypergeom([1/2, n+3],[1],4/3))/((n+3)*(n+5)*(n+6)*(7+n))

G.f.: (2*x-1)*((x+1)^(1/2)*(1-3*x)^(1/2)*(x-1)*(x^2+2*x-1)+x^4-4*x^3-2*x^2+4*x-1)/(2*x^8). (End)

Conjecture: -(n+7)*(3*n-31)*a(n) +3*(-n^2-35*n-76)*a(n-1) +2*(32*n^2+27*n-459)*a(n-2) +(-47*n^2+286*n-204)*a(n-3) -3*(37*n-51)*(n-2)*a(n-4)=0. - R. J. Mathar, Jun 23 2013

Crossrefs

Cf. A026148.

Equals T(n, n-1), where T is the array in A026323.

Sequence in context: A349488 A055544 A126285 * A005717 A333106 A025266

Adjacent sequences: A026160 A026161 A026162 * A026164 A026165 A026166

Keyword

nonn

Author

Clark Kimberling

Status

approved