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A001332 Bernoulli(2*n) * (2*n + 1)!.
(Formerly M3710 N1516)
5

%I M3710 N1516

%S 1,1,-4,120,-12096,3024000,-1576143360,1525620096000,

%T -2522591034163200,6686974460694528000,-27033456071346536448000,

%U 160078872315904478576640000,-1342964491649083924630732800000,15522270327163593186886877184000000

%N Bernoulli(2*n) * (2*n + 1)!.

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001332/b001332.txt">Table of n, a(n) for n = 0..50</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%F 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

%F 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

%F a(n) = A129814(2*n). - _Michael Somos_, Mar 29 2011

%t Table[BernoulliB[2*n]*(2*n + 1)!, {n, 0, 20}] (* _T. D. Noe_, Jun 28 2012 *)

%o (PARI) {a(n) = if( n<0, 0, (2*n + 1)! * bernfrac( 2*n))} /* _Michael Somos_, Oct 08 2003 */

%Y Cf. A129814.

%K sign,nice

%O 0,3

%A _N. J. A. Sloane_

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Last modified November 15 19:54 EST 2018. Contains 317240 sequences. (Running on oeis4.)