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

%I

%S 1,2,6,16,45,126,356,1008,2862,8140,23188,66144,188916,540216,1546560,

%T 4432512,12717513,36526626,105016686,302228080,870613689,2510249302,

%U 7244285436,20924179920,60487084775,174994990326,506669921982

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

%F Conjectures from _Mark van Hoeij_, Oct 30 2011: (Start)

%F 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))

%F 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)

%F 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

%Y Cf. A026148.

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

%K nonn

%O 1,2

%A _Clark Kimberling_

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Last modified January 16 09:13 EST 2021. Contains 340204 sequences. (Running on oeis4.)