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A132745
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Row sums of (A008550 formatted as a triangular array).
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4
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1, 2, 3, 5, 11, 32, 114, 467, 2130, 10642, 57629, 335381, 2082582, 13716502, 95352529, 696790819, 5334094259, 42649956716, 355261078352, 3075741331481, 27620835538407, 256810928552476, 2468108094076860, 24481671811988907, 250296546308500181, 2634309876797453868, 28509045368598994348
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history;
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Hypergeometric2F1([1-n+k, k-n], [2], k).
a(n) = Sum_{k=0..n} Hypergeometric2F1([1-k, -k], [2], n-k).
a(n) = 1 + Sum_{k=1..n} Sum_{j=0..k-1} binomial(k,j)^2 * ((k-j)*(n-k)^j/(k*(j+1))).
a(n) = 1 + Sum_{k=1..n} Sum_{j=0..k-1} A001263(k, k-j) * (n-k)^j. (End)
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MATHEMATICA
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Table[Sum[Hypergeometric2F1[1-k, -k, 2, n-k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Feb 16 2021 *)
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PROG
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(Sage)
def A243631(n, k): return 1 if n==0 else sum( binomial(n, j)^2*k^j*(n-j)/(n*(j+1)) for j in [0..n-1])
(Magma)
A243631:= func< n, k | n eq 0 select 1 else (&+[ Binomial(n, j)^2*k^j*(n-j)/(n*(j+1)): j in [0..n-1]]) >;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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