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A051715
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Denominators of table a(n,k) read by antidiagonals: a(0,k) = 1/(k+1), a(n+1,k) = (k+1)(a(n,k)-a(n,k+1)), n >= 0, k >= 0.
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13
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1, 2, 2, 3, 3, 6, 4, 4, 6, 1, 5, 5, 20, 30, 30, 6, 6, 15, 20, 30, 1, 7, 7, 42, 35, 140, 42, 42, 8, 8, 28, 84, 105, 28, 42, 1, 9, 9, 72, 84, 1, 105, 140, 30, 30, 10, 10, 45, 120, 140, 28, 105, 20, 30, 1, 11, 11, 110, 495, 3960, 924, 231, 165, 220, 66, 66, 12, 12, 66, 55, 495, 264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Leading column gives the Bernoulli numbers A027641/A027642.
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LINKS
| M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.
Index entries for sequences related to Bernoulli numbers.
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EXAMPLE
| Table begins:
1 1/2 1/3 1/4 1/5 1/6 1/7 ...
1/2 1/3 1/4 1/5 1/6 1/7 ...
1/6 1/6 3/20 2/15 5/42 ...
0 1/30 1/20 2/35 5/84 ...
-1/30 -1/30 -3/140 -1/105 ...
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MATHEMATICA
| nmax = 12; a[0, k_] := 1/(k+1); a[n_, k_] := a[n, k] = (k+1)(a[n-1, k]-a[n-1, k+1]); Denominator[ Flatten[ Table[ a[n-k, k], {n, 0, nmax}, {k, n, 0, -1}]]](* From Jean-François Alcover, Nov 28 2011 *)
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CROSSREFS
| Rows 2, 3, 4 give A026741/A045896, A051712/A051713, A051722/A051723, columns 0, 1, 2, 3 give A000367/A002445, A051716/A051717, A051718/A051719, A051720/A051721.
Sequence in context: A103403 A052473 A165122 * A143269 A036817 A175175
Adjacent sequences: A051712 A051713 A051714 * A051716 A051717 A051718
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KEYWORD
| nonn,frac,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
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