A051718 Numerators of column 2 of table described in A051714/A051715.

1, 1, 3, 1, -3, -1, 1, 1, 1, -5, -1017, 691, 601, -7, -809, 3617, 922191, -43867, -6132631, 174611, 12988703, -854513, -1552922421, 236364091, 1139644561, -8553103, -7089687053, 23749461029, 378639019356093, -8615841276005

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy
• nice
• frac

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..627
• M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.

Crossrefs

Cf. A051714, A051715, A051719.

Programs

Mathematica

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 *)

Formula

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

Extensions

More terms from James Sellers, Dec 08 1999