A001332 a(n) = Bernoulli(2*n) * (2*n + 1)!. (Formerly M3710 N1516)

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

Offset

0,3

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.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A129814.

Sequence in context: A068204 A203033 A307935 * A071304 A213957 A006607

Adjacent sequences: A001329 A001330 A001331 * A001333 A001334 A001335

Keyword

sign,nice

Author

N. J. A. Sloane

Status

approved