login
A230262
Numerators of Akiyama-Tanigawa algorithm applied to harmonic numbers, written by antidiagonals.
0
1, 3, -1, 11, -2, 1, 25, -3, 1, 0, 137, -4, 3, 1, -1, 49, -5, 2, 1, -1, 0, 363, -6, 5, 2, -3, -1, 1, 761, -7, 3, 5, -1, -1, 1, 0, 7129, -8, 7, 5, 0, -4, 1, 1, -1, 7381, -9, 4, 7, 1, -1, -1, 1, -1, 0, 83711, -10, 9, 28, 49, -29, -5, 8, 1, -5, 5
OFFSET
0,2
COMMENTS
Leading column gives the Bernoulli numbers: A027641(n)/A027642(n). In A051714, A164555 must be written instead of A027641.
LINKS
M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, Vol 3 (2000), #00.2.9.
EXAMPLE
Numerators of
1, 3/2, 11/6, 25/12,...
-1/2, -2/3, -3/4, -4/5,...
1/6, 1/6, 3/20, 2/15,... =A026741(n+1)/A045896(n+1)
0, 1/30, 1/20, 2/35,... =A194531/A193220.
MATHEMATICA
t[1, k_] := HarmonicNumber[k]; t[n_, k_] := t[n, k] = k*(t[n-1, k] - t[n-1, k+1]); Table[t[n-k+1, k] // Numerator, {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Nov 15 2013 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Paul Curtz, Nov 09 2013
EXTENSIONS
More terms from Jean-François Alcover, Nov 15 2013
STATUS
approved