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%I #12 Mar 24 2020 19:41:49
%S 1,1,4,14,72,424,2960,23568,211456,2109056,23150592,277315840,
%T 3599704064,50331030528,754122723328,12054165272576,204743835156480,
%U 3682557441114112,69920454322356224,1397542619388248064,29331932133035081728,644973249444408197120
%N E.g.f. exp(-x)*cosh(x)/(1-x)^2.
%C A088127(n)+A037256(n)=(n+1)! Binomial transform is A088128.
%H Vincenzo Librandi, <a href="/A088127/b088127.txt">Table of n, a(n) for n = 0..200</a>
%F Recurrence: a(n) = 2*(n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3). - _Vaclav Kotesovec_, Oct 14 2012
%F a(n) ~ n!*n*(1+1/e^2)/2. - _Vaclav Kotesovec_, Oct 14 2012
%t Table[n!*SeriesCoefficient[E^(-x)*Cosh[x]/(1-x)^2,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 14 2012 *)
%t With[{nn=30},CoefficientList[Series[Exp[-x] Cosh[x]/(1-x)^2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 24 2020 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(-x)*cosh(x)/(1-x)^2)) \\ _Joerg Arndt_, May 10 2013
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 19 2003