OFFSET
0,5
COMMENTS
From Peter Luschny, Apr 21 2009: (Start)
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
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
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 *)
PROG
(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 */
(Magma) [Bernoulli(n) * Factorial(n+1): n in [0..100]]; // Vincenzo Librandi, Mar 29 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, May 20 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, May 28 2007
STATUS
approved