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 A119884 #23 Jan 25 2025 02:12:41
%S A119884 1,1,1,3,17,85,449,3143,26529,238761,2337089,25707979,311198513,
%T A119884 4045580669,56438768385,846581525775,13564695924545,230599830717265,
%U A119884 4148392073235329,78819449391471251,1576759359017662545,33111946539370913445,728393474991766957889
%N A119884 Expansion of e.g.f. sech(x)/(1-x).
%C A119884 Transform of n! under the matrix A119879.
%H A119884 G. C. Greubel, <a href="/A119884/b119884.txt">Table of n, a(n) for n = 0..445</a>
%F A119884 a(n) = Sum_{k=0..n} A119879(n,k) * k!.
%F A119884 E.g.f.: 1/U(0) where U(k) = 1 - x/(1 - x/(x - (2*k+1)*(2*k+2)/U(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Oct 17 2012
%F A119884 a(n) ~ n! * 2*exp(1)/(exp(2)+1). - _Vaclav Kotesovec_, Sep 25 2013
%F A119884 a(n) = n! * Sum_{j=0..n} A122045(j)/j!. - _G. C. Greubel_, Jun 07 2023
%p A119884 restart: G(x):= sech(x)/(1-x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..20); # _Zerinvary Lajos_, Apr 03 2009
%t A119884 CoefficientList[Series[1/((1-x)*(E^x/2+E^(-x)/2)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 25 2013 *)
%t A119884 Table[n!*Sum[EulerE[j]/j!, {j,0,n}], {n,0,40}] (* _G. C. Greubel_, Jun 07 2023 *)
%o A119884 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( 1/((1-x)*Cosh(x)) ))); // _G. C. Greubel_, Jun 07 2023
%o A119884 (SageMath)
%o A119884 def A119884(n): return factorial(n)*sum(euler_number(j)/factorial(j) for j in range(n+1))
%o A119884 [A119884(n) for n in range(41)] # _G. C. Greubel_, Jun 07 2023
%Y A119884 Cf. A119879, A122045.
%K A119884 easy,nonn
%O A119884 0,4
%A A119884 _Paul Barry_, May 26 2006