A001332 a(n) = Bernoulli(2*n) * (2*n + 1)!.

1, 1, -4, 120, -12096, 3024000, -1576143360, 1525620096000, -2522591034163200, 6686974460694528000, -27033456071346536448000, 160078872315904478576640000, -1342964491649083924630732800000, 15522270327163593186886877184000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• nice

References

• G. S. Kazandzidis, On a Matrix and a Class of Polynomials, Bulletin de la Société Mathématique de Grèce, Nouvelle Série - Vol. 6 I, Fasc. 1, (1965), pp. 105-126.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..50
• Zentralblatt, Review of Kazandzidis, On a Matrix and a Class of Polynomials.
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Cf. A129814.

Programs

Mathematica

Table[BernoulliB[2*n]*(2*n + 1)!, {n, 0, 20}] (* T. D. Noe, Jun 28 2012 *)

PARI

{a(n) = if( n<0, 0, (2*n + 1)! * bernfrac( 2*n))} /* Michael Somos, Oct 08 2003 */

Formula

Lacunary e.g.f: x / (exp(x) - 1) + x / 2 = Sum_{k>=0} a(k) * x^(2*k) / ((2*k)! * (2*k + 1)!). - Michael Somos, Mar 29 2011

a(n) = determinant of the 2n X 2n matrix ( d(i,j) = binomial( i+1, i-j+2) if j < i+2 else 0 ). - Michael Somos, Oct 08 2003

a(n) = A129814(2*n). - Michael Somos, Mar 29 2011