%I #25 Dec 18 2022 09:11:53
%S 6,60,126,120,66,16380,6,4080,7182,3300,138,32760,6,1740,42966,8160,6,
%T 34545420,6,270600,37926,1380,282,1113840,66,3180,21546,3480,354,
%U 1703601900,6,16320,194166,60,4686,5043631320,6,60,9954,9200400,498,142981020,6
%N Write cosec x = 1/x + Sum e_n x^(2n-1)/(2n-1)!; sequence gives denominators of e_n.
%C Denominator of [2^(2n-1) - 1] * Bernoulli(2n)/n.
%C Equals the denominators of the LS1[-2*m,n=1] matrix coefficients of A160487 for m = 1, 2, ... - _Johannes W. Meijer_, May 24 2009
%C The products of the first n terms of this sequence appear in the denominators of the a(n) formulas of the right hand columns of triangle A161739. See A000292 (n=1), A107963 (n=2), A161740 (n=3) and A161741 (n=4). The next six values of n show that this pattern persists. - _Johannes W. Meijer_, Oct 22 2009
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).
%H Robert Israel, <a href="/A036283/b036283.txt">Table of n, a(n) for n = 1..10000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).
%F Apparently a(n) = 6*A202318(n). - _Hugo Pfoertner_, Dec 18 2022
%e x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+...
%p seq(denom((2^(2*n-1)-1)*bernoulli(2*n)/n),n=1..100); # _Robert Israel_, Oct 14 2016
%o (PARI) a(n) = denominator((2^(2*n-1)-1)*bernfrac(2*n)/n) \\ _Hugo Pfoertner_, Dec 18 2022
%Y Cf. A036280-A036282.
%Y Cf. A000292, A006953, A107963, A160487, A161739, A161740, A161741.
%K nonn,frac,easy
%O 1,1
%A _N. J. A. Sloane_
%E Title corrected and offset changed by _Johannes W. Meijer_, May 21 2009
%E More terms, and edited by _Robert Israel_, Oct 14 2016