A076549 Numerator of (2n+1)(2n+2) B_{2n}, where B_n are the Bernoulli numbers. Also numerators of the asymptotic expansion of the polygamma function psi'''(z).

2, 3, 2, -1, 4, -3, 10, -691, 280, -10851, 438670, -1222277, 3418052, -1181820455, 1077690978, -23749461029, 137853460416080, -84802531453387, 541314450257070, -26315271553053477373, 761798417598805340

Offset: 0

Author

Ralf Stephan, Oct 19 2002

Keywords

• easy
• frac
• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Abramowitz and Stegun, Handbook of mathematical functions, p. 260 (6.4.14)
• Abramowitz and Stegun, Handbook of mathematical functions, p. 260 (6.4.14)

Crossrefs

Denominators are in A006956. Cf. A002427/A006955.

Programs

Mathematica

Join[{2, 3}, Table[Numerator[(4 n^2 + 6 n + 2) BernoulliB[2 n]], {n, 1, 30}]] (* Vincenzo Librandi, Aug 02 2013 *)