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A051720 Numerators of column 3 of table described in A051714/A051715. 5

%I

%S 1,1,2,2,-1,-4,-1,8,7,-44,-2663,368,1247,-244,-1511,43416,1623817,

%T -276356,-10405289,-21376,21491081,32209348,-2523785339,-107638072,

%U 1827648887,842271812,-11254630547,-17380760743952,596303510772251

%N Numerators of column 3 of table described in A051714/A051715.

%H Seiichi Manyama, <a href="/A051720/b051720.txt">Table of n, a(n) for n = 0..626</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(4*x))/(1-exp(x))^4+13/(3*(1-exp(x)))-7/(2*(1-exp(x))^2)+1/(1-exp(x))^3-13/12. - _Vladimir Kruchinin_, Nov 03 2015

%t a[0, k_] := 1/(k+1); a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); a[n_] := a[n, 3] // Numerator; Table[a[n], {n, 0, 28}] (* _Jean-Fran├žois Alcover_, Sep 17 2012 *)

%Y Cf. A051721.

%K sign,easy,nice

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Dec 08 1999

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Last modified January 24 10:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)