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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.

Index entries for sequences related to Bernoulli numbers.

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-Fran├žois 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

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Dec 07 1999

STATUS

approved

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Last modified December 9 02:36 EST 2016. Contains 278959 sequences.