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 A009132 #24 Dec 29 2024 21:41:14
%S A009132 1,-1,2,-7,31,-161,976,-6847,54797,-493201,4932046,-54252551,
%T A009132 651030667,-8463398737,118487582396,-1777313736031,28437019776601,
%U A009132 -483429336202337,8701728051642202,-165332832981201991,3306656659624039991
%N A009132 Expansion of e.g.f. cosh(log(1+x))/exp(x).
%H A009132 G. C. Greubel, <a href="/A009132/b009132.txt">Table of n, a(n) for n = 0..250</a>
%F A009132 a(n) = (-1)^n/2*floor(n!*exp(1)-n+1), n>0. - _Vladeta Jovovic_, Aug 17 2002
%F A009132 E.g.f.: (2+2*x+x^2)/(2*(1+x)*exp(x)) = (1+x/G(0))/2 ; G(k) = 1 - 1/(1 + x + x^2 - (x*(1+x))^2/(x*(1+x) - (k+1)/(1 + x/G(k+1)))) ; (continued fraction). - _Sergei N. Gladkovskii_, Dec 28 2011
%t A009132 With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]]/Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 28 2018 *)
%o A009132 (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/exp(x))) \\ _G. C. Greubel_, Jul 28 2018
%o A009132 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Exp(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018
%Y A009132 Cf. A009578.
%K A009132 sign,easy
%O A009132 0,3
%A A009132 _R. H. Hardin_
%E A009132 Extended with signs by _Olivier Gérard_, Mar 15 1997