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A051714
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Numerators 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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15
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1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, -1, 1, 1, 2, 1, -1, 0, 1, 1, 5, 2, -3, -1, 1, 1, 1, 3, 5, -1, -1, 1, 0, 1, 1, 7, 5, 0, -4, 1, 1, -1, 1, 1, 4, 7, 1, -1, -1, 1, -1, 0, 1, 1, 9, 28, 49, -29, -5, 8, 1, -5, 5, 1, 1, 5, 3, 8, -7, -9, 5, 7, -5, 5, 0, 1, 1, 11, 15, 27, -28, -343, 295, 200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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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]); Numerator[ 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: A061653 A069226 A016565 * A023593 A117544 A030393
Adjacent sequences: A051711 A051712 A051713 * A051715 A051716 A051717
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KEYWORD
| sign,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 07 1999
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