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A292901
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Triangle read by rows, a generalization of the Bernoulli numbers, the denominators for n>=0 and 0<=k<=n.
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1
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1, 1, 2, 1, 2, 6, 1, 2, 3, 1, 1, 2, 12, 3, 30, 1, 2, 24, 9, 20, 1, 1, 2, 48, 54, 80, 10, 42, 1, 2, 96, 324, 8640, 200, 105, 1, 1, 2, 192, 1944, 3840, 36000, 525, 35, 30, 1, 2, 384, 11664, 1244160, 720000, 756000, 3675, 168, 1
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history;
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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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EXAMPLE
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Triangle starts:
[0], 1
[1], 1, 2
[2], 1, 2, 6
[3], 1, 2, 3, 1
[4], 1, 2, 12, 3, 30
[5], 1, 2, 24, 9, 20, 1
[6], 1, 2, 48, 54, 80, 10, 42
[7], 1, 2, 96, 324, 8640, 200, 105, 1
[8], 1, 2, 192, 1944, 3840, 36000, 525, 35, 30
[9], 1, 2, 384, 11664, 1244160, 720000, 756000, 3675, 168, 1
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MAPLE
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for n from 0 to 9 do seq(denom(B(n, k)), k=0..n) od;
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MATHEMATICA
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B[0, 0] = 1; B[n_, k_] := Sum[(-1)^(j-n)/(j+1) Binomial[k+1, j+1] Sum[i^n (j-i+1)^(k-n), {i, 0, j}], {j, 0, k}]; Table[B[n, k] // Denominator, {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 14 2019, from Maple *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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