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A110490
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Diagonal sums of a triangle based on the Catalan numbers.
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2
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1, 1, 3, 7, 20, 59, 185, 600, 2003, 6833, 23727, 83606, 298313, 1076155, 3920823, 14416987, 53482012, 200151737, 755894009, 2882782933, 11115015138, 43400057683, 172016505877, 694208585423, 2863726993748, 12130698802645
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-2*k)} 2*(j+1)*(k-1)^j*C(2*(n-2*k)+1, n-2*k-j)/(n-2*k+j+2).
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MATHEMATICA
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T[n_, 0] := CatalanNumber[n]; T[n_, 1] := CatalanNumber[n]; T[n_, n_] := 1; T[n_, k_] := Sum[2*(j + 1)*(k - 1)^j*Binomial[2 (n - k) + 1, n - k - j]/(n - k + j + 2), {j, 0, n - k}]; Join[{1, 1}, Table[Sum[T[n - k, k], {k, 0, n}], {n, 2, 50}]] (* G. C. Greubel, Aug 29 2017 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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