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, 15522270327163593186886877184000000

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

Table of n, a(n) for n=0..26.

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

Maple

# We deliberately refrain from using Bernoulli numbers and factorials to describe the underlying structure.
A129814 := proc(n) local L, i, j; L:=[seq(mul(`if`(j=i, 1, j), j=1..n+1), i=1..n+1)];
while nops(L)>1 do L:=[seq((L[i]-L[i-1])*(i-1), i=2..nops(L))]od; L[1] end:
seq(A129814(n), n=0..26);  # Peter Luschny, Jul 12 2026

Mathematica

Table[BernoulliB[n](n+1)!, {n, 0, 30}] (* Harvey P. Dale, Jan 18 2013 *)
(* Alternative: *)
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, A137777, A159749.

Sequence in context: A337112 A357560 A013037 * A129825 A267441 A264883

Adjacent sequences: A129811 A129812 A129813 * A129815 A129816 A129817

Keyword

sign,easy,changed

Author

Paul Curtz, May 20 2007

Extensions

Edited and extended by Klaus Brockhaus, May 28 2007

Status

approved