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A185963
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Row sums of number triangle A185962.
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5
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1, 0, -2, -3, 0, 7, 11, 1, -24, -40, -7, 82, 145, 37, -279, -524, -174, 945, 1888, 767, -3185, -6783, -3244, 10676, 24301, 13330, -35567, -86823, -53615, 117672, 309366, 212101, -386224, -1099385, -827997, 1255937, 3896480, 3197152, -4039199, -13773374
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1-x)^2/(1-2x+3x^2-x^3).
a(n) = Sum_{k=0..n} Sum_{i=0..(2k+2)} C(2k+2,i)*Sum_{j=0..(n-k-i)} C(k+j,j)*C(j,n-k-i-j)*(-1)^(n-k-j).
a(n) = hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27). - Peter Luschny, Nov 03 2017
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EXAMPLE
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G.f. = 1 - 2*x^2 - 3*x^3 + 7*x^5 + 11*x^6 + x^7 - 24*x^8 - 40*x^9 + ...
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MAPLE
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a := n -> hypergeom([(n+1)/2, n/2+1, -n], [1/3, 2/3], 4/27):
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MATHEMATICA
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PROG
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(PARI) x='x+O('x^50); Vec((1-x)^2/(1-2*x+3*x^2-x^3)) \\ G. C. Greubel, Jul 23 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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