This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036283 #25 Dec 18 2022 09:11:53 %S A036283 6,60,126,120,66,16380,6,4080,7182,3300,138,32760,6,1740,42966,8160,6, %T A036283 34545420,6,270600,37926,1380,282,1113840,66,3180,21546,3480,354, %U A036283 1703601900,6,16320,194166,60,4686,5043631320,6,60,9954,9200400,498,142981020,6 %N A036283 Write cosec x = 1/x + Sum e_n x^(2n-1)/(2n-1)!; sequence gives denominators of e_n. %C A036283 Denominator of [2^(2n-1) - 1] * Bernoulli(2n)/n. %C A036283 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 A036283 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 A036283 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 A036283 Robert Israel, <a href="/A036283/b036283.txt">Table of n, a(n) for n = 1..10000</a> %H A036283 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 A036283 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 A036283 Apparently a(n) = 6*A202318(n). - _Hugo Pfoertner_, Dec 18 2022 %e A036283 x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+... %p A036283 seq(denom((2^(2*n-1)-1)*bernoulli(2*n)/n),n=1..100); # _Robert Israel_, Oct 14 2016 %o A036283 (PARI) a(n) = denominator((2^(2*n-1)-1)*bernfrac(2*n)/n) \\ _Hugo Pfoertner_, Dec 18 2022 %Y A036283 Cf. A036280-A036282. %Y A036283 Cf. A000292, A006953, A107963, A160487, A161739, A161740, A161741. %K A036283 nonn,frac,easy %O A036283 1,1 %A A036283 _N. J. A. Sloane_ %E A036283 Title corrected and offset changed by _Johannes W. Meijer_, May 21 2009 %E A036283 More terms, and edited by _Robert Israel_, Oct 14 2016