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A001332 Bernoulli(2*n) * (2*n + 1)!.
(Formerly M3710 N1516)
4
1, 1, -4, 120, -12096, 3024000, -1576143360, 1525620096000, -2522591034163200, 6686974460694528000, -27033456071346536448000, 160078872315904478576640000, -1342964491649083924630732800000, 15522270327163593186886877184000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

G. S. Kazandzidis: On a Matrix and a Class of Polynomials. Bulletin de la Societe Mathematique de Grece. Nouvelle Serie - 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

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: A002702 A068204 A203033 * A071304 A213957 A006607

Adjacent sequences:  A001329 A001330 A001331 * A001333 A001334 A001335

KEYWORD

sign,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 23 18:52 EST 2018. Contains 299585 sequences. (Running on oeis4.)