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A184884
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Diagonal sums of number triangle A184883.
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3
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1, 1, 2, 6, 11, 27, 60, 132, 301, 669, 1502, 3370, 7543, 16919, 37912, 84968, 190457, 426841, 956698, 2144238, 4805827, 10771315, 24141588, 54108332, 121272549, 271806901, 609198390, 1365390546, 3060236911, 6858880431, 15372743856, 34454786384, 77223188593, 173079605553, 387921692082, 869445237846
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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-x-2*x^2-2*x^3+x^4-x^5).
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..k} C(2*n-4*k,j)*C(k,j)*2^j.
a(n) = Sum_{k=0..floor(n/2)} Hypergeometric2F1([-k, 2*(k-n)], [1], 2). - G. C. Greubel, Nov 19 2021
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MATHEMATICA
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LinearRecurrence[{1, 2, 2, -1, 1}, {1, 1, 2, 6, 11}, 45] (* G. C. Greubel, Nov 19 2021 *)
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PROG
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(Magma)
A184883:= func< n, k | (&+[Binomial(k, j)*Binomial(2*(n-k), j)*2^j: j in [0..k]]) >;
(Sage)
def A184883(n, k): return simplify( hypergeometric([-k, 2*(k-n)], [1], 2) )
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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