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%I #27 Sep 19 2016 11:43:12
%S 1,1,3,1,-3,-1,1,1,1,-5,-1017,691,601,-7,-809,3617,922191,-43867,
%T -6132631,174611,12988703,-854513,-1552922421,236364091,1139644561,
%U -8553103,-7089687053,23749461029,378639019356093,-8615841276005
%N Numerators of column 2 of table described in A051714/A051715.
%H Seiichi Manyama, <a href="/A051718/b051718.txt">Table of n, a(n) for n = 0..627</a>
%H M. Kaneko, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/KANEKO/AT-kaneko.html">The Akiyama-Tanigawa algorithm for Bernoulli numbers</a>, J. Integer Sequences, 3 (2000), #00.2.9.
%F a(n) = numerator(n! * [x^n] f(x)) where f(x) = -(x*exp(3*x))/(1-exp(x))^3+5/(2*(1-exp(x)))-1/(1-exp(x))^2-5/6. - _Vladimir Kruchinin_, Nov 03 2015
%t nmax = 29; a[0, k_] := 1/(k + 1); a[n_, k_] := a[n, k] = (k + 1)*(a[n - 1, k] - a[n - 1, k + 1]); Table[a[n, k], {n, 0, nmax}, {k, 0, nmax}] [[All, 3]] // Numerator (* _Jean-François Alcover_, Oct 08 2012 *)
%Y Cf. A051714, A051715, A051719.
%K sign,easy,nice,frac
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Dec 08 1999
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