A129814 a(n) = Bernoulli(n) * (n+1)!.

1, -1, 1, 0, -4, 0, 120, 0, -12096, 0, 3024000, 0, -1576143360, 0, 1525620096000, 0, -2522591034163200, 0, 6686974460694528000, 0, -27033456071346536448000, 0, 160078872315904478576640000, 0, -1342964491649083924630732800000, 0

Offset: 0

Author

Paul Curtz, May 20 2007

Keywords

• sign
• easy

Comments

From Peter Luschny, Apr 21 2009: (Start)

Reading A137777 and A159749 as a triangular sequence:

2*a(n) = A137777(n, 0) for n > 0.

2*a(n) = (-1)^n*A159749(n, 0) for n >= 0. (End)

Links

• Eric Weisstein's World of Mathematics, Bernoulli Number
• Eric Weisstein's World of Mathematics, Polygamma Function

Crossrefs

Cf. A001332.

Programs

Magma

[Bernoulli(n) * Factorial(n+1): n in [0..100]]; // Vincenzo Librandi, Mar 29 2011

Mathematica

Table[BernoulliB[n](n+1)!,{n,0,30}] (* Harvey P. Dale, Jan 18 2013 *)
Table[SeriesCoefficient[-2 x - PolyGamma[2, 1/x] / x^2, {x, 0, n}, Assumptions -> x > 0] n!, {n, 0, 30}] (* Vladimir Reshetnikov, Apr 24 2013 *)

PARI

{for(n=0, 25, print1(bernfrac(n)*(n+1)!, ","))}

PARI

{a(n) = if( n<0, 0, (n + 1)! * bernfrac( n))} /* Michael Somos, Mar 29 2011 */

Formula

a(2*n) = A001332(n).

E.g.f.: -2 x - psi_2(1/x) / x^2, where psi_n(z) is the polygamma function, psi_n(z) = (d/dz)^{n+1} log(Gamma(z)). - Vladimir Reshetnikov, Apr 24 2013

Extensions

Edited and extended by Klaus Brockhaus, May 28 2007