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

1, 1, 2, 2, -1, -4, -1, 8, 7, -44, -2663, 368, 1247, -244, -1511, 43416, 1623817, -276356, -10405289, -21376, 21491081, 32209348, -2523785339, -107638072, 1827648887, 842271812, -11254630547, -17380760743952, 596303510772251

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy
• nice

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..626
• M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.

Crossrefs

Cf. A051721.

Programs

Mathematica

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-François Alcover, Sep 17 2012 *)

Formula

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

Extensions

More terms from James Sellers, Dec 08 1999