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 A129814 a(n) = Bernoulli(n) * (n+1)!. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 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 Cf. A001332. Sequence in context: A247119 A228557 A013037 * A129825 A267441 A264883 Adjacent sequences:  A129811 A129812 A129813 * A129815 A129816 A129817 KEYWORD sign,easy AUTHOR Paul Curtz, May 20 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, May 28 2007 STATUS approved

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