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 A009575 #35 Jan 22 2018 02:40:47
%S A009575 0,0,2,-6,26,-140,894,-6594,55152,-515808,5334480,-60453360,745035840,
%T A009575 -9921337920,141972324480,-2172695011200,35410730342400,
%U A009575 -612356632473600,11198955424204800,-215960417122867200,4379675205233664000
%N A009575 E.g.f. sinh(log(1+x))*log(1+x).
%C A009575 abs(a(n)) is the number of cycles in all permutations of n elements with an even number of cycles. - _Vladeta Jovovic_, Sep 06 2007
%H A009575 G. C. Greubel, <a href="/A009575/b009575.txt">Table of n, a(n) for n = 0..448</a>
%F A009575 E.g.f.: (1+x)*x/2*U(0) where U(k)= 1 - 1/((1+x)^2 - x*(1+x)^4*(k+1)/(x*(1+x)^2*(k+1) + (k+2)/U(k+1))) ; (continued fraction, 3rd kind, 3-step). - _Sergei N. Gladkovskii_, Sep 25 2012
%F A009575 a(n) ~ n! * (-1)^n * log(n) / 2 * (1 + gamma/log(n)), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Jan 24 2015
%e A009575 a(n) = ((-1)^n*(n!*h(n) + (n-2)!))/2, n > 1, where h(n) = Sum_{k=1..n} 1/k. - _Gary Detlefs_, Aug 31 2011
%t A009575 nn=30; Range[0, nn]! CoefficientList[Series[Sinh[Log[1 + x]]*Log[1 + x], {x, 0, nn}], x]
%t A009575 CoefficientList[Series[(x*(2 + x)*Log[1 + x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)
%o A009575 (PARI) x='x+O('x^66);
%o A009575 concat([0,0],Vec(serlaplace(sinh(log(1+x))*log(1+x))))
%Y A009575 Cf. A000254.
%K A009575 sign,easy
%O A009575 0,3
%A A009575 _R. H. Hardin_
%E A009575 Extended with signs by _Olivier Gérard_, Mar 15 1997