A129814 - OEIS

%I #23 Sep 08 2022 08:45:30

%S 1,-1,1,0,-4,0,120,0,-12096,0,3024000,0,-1576143360,0,1525620096000,0,

%T -2522591034163200,0,6686974460694528000,0,-27033456071346536448000,0,

%U 160078872315904478576640000,0,-1342964491649083924630732800000,0

%N a(n) = Bernoulli(n) * (n+1)!.

%C From _Peter Luschny_, Apr 21 2009: (Start)

%C Reading A137777 and A159749 as a triangular sequence:

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>

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

%F 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

%t Table[BernoulliB[n](n+1)!,{n,0,30}] (* _Harvey P. Dale_, Jan 18 2013 *)

%t 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 *)

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

%o (PARI) {a(n) = if( n<0, 0, (n + 1)! * bernfrac( n))} /* _Michael Somos_, Mar 29 2011 */

%o (Magma) [Bernoulli(n) * Factorial(n+1): n in [0..100]]; // _Vincenzo Librandi_, Mar 29 2011

%Y Cf. A001332.

%K sign,easy

%O 0,5

%A _Paul Curtz_, May 20 2007

%E Edited and extended by _Klaus Brockhaus_, May 28 2007