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A100621
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Denominator of Cotesian number C(n,0).
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10
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1, 2, 6, 8, 90, 288, 840, 17280, 28350, 89600, 598752, 17418240, 63063000, 402361344000, 5003856000, 295206912, 976924698750, 342372925440000, 15209113920000, 5377993912811520000, 96852084769440, 89903156428800000, 37556196837868800000, 73570956727261593600000
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OFFSET
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0,2
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REFERENCES
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Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
See A002176 for further references.
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LINKS
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EXAMPLE
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0, 1/2, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/63063000, 8181904909/402361344000, ... = A100620/A100621 = A002177/A002176 (the latter is not in lowest terms)
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MATHEMATICA
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cn[n_, 0] := Sum[n^j*StirlingS1[n, j]/(j + 1), {j, 1, n + 1}]/n!; cn[n_, n_] := cn[n, 0]; cn[n_, k_] := 1/n!*Binomial[n, k]*Sum[n^(j + m)*StirlingS1[k, j]*StirlingS1[n - k, m]/((m + 1)*Binomial[j + m + 1, m + 1]), {m, 1, n}, {j, 1, k + 1}]; Table[cn[n, 0] // Denominator, {n, 0, 23}] (* Jean-François Alcover, Jan 16 2013 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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