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 A051714 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. 21
 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, -44, -1017, 691, -691 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Leading column gives the Bernoulli numbers A164555/A027642. - corrected by Paul Curtz, Apr 17 2014 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9. 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 ... MAPLE a:= proc(n, k) option remember;       `if`(n=0, 1/(k+1), (k+1)*(a(n-1, k)-a(n-1, k+1)))     end: seq(seq(numer(a(n, d-n)), n=0..d), d=0..12); # Alois P. Heinz, Apr 17 2013 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}]]](* Jean-François Alcover, Nov 28 2011 *) 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. Denominators are in A051715. Sequence in context: A061653 A069226 A016565 * A023593 A117544 A030393 Adjacent sequences:  A051711 A051712 A051713 * A051715 A051716 A051717 KEYWORD sign,frac,nice,easy,tabl,look AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 07 1999 STATUS approved

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Last modified June 25 08:21 EDT 2019. Contains 324347 sequences. (Running on oeis4.)