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A026163 Sum{T(k,k-1)}, k = 1,2,...,n, where T is the array in A026148. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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) -  a(n) and G.f. based on guessed recurrence - Mark van Hoeij, Oct 30 2011.

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

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

Sequence in context: A209629 A055544 A126285 * A005717 A025266 A074403

Adjacent sequences:  A026160 A026161 A026162 * A026164 A026165 A026166

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)