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A193385 Expansion of e.g.f. cosh( x^2/2 )/ (1-x).

%I A193385 #20 Sep 08 2022 08:45:58
%S A193385 1,1,2,6,27,135,810,5670,45465,409185,4091850,45010350,540134595,
%T A193385 7021749735,98304496290,1474567444350,23593081136625,401082379322625,
%U A193385 7219482827807250,137170173728337750,2743403475221484075
%N A193385 Expansion of e.g.f. cosh( x^2/2 )/ (1-x).
%H A193385 G. C. Greubel, <a href="/A193385/b193385.txt">Table of n, a(n) for n = 0..449</a>
%F A193385 a(n) ~ cosh( 1/2 ) * n!.
%F A193385 a(n) = (A000266(n) + A130905(n)) / 2.
%p A193385 a:=series(cosh(x^2/2)/(1-x),x=0,21): seq(n!*coeff(a,x,n),n=0..20); # _Paolo P. Lava_, Mar 27 2019
%t A193385 With[{nn=30},CoefficientList[Series[Cosh[x^2/2]/(1-x),{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, May 01 2012 *)
%o A193385 (PARI) {a(n) = if( n<0, 0, n! * polcoeff( cosh( x^2 / 2 + x * O(x^n)) / (1 - x), n))}
%o A193385 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(x^2/2)/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2018
%Y A193385 Cf. A000266, A130905.
%K A193385 nonn
%O A193385 0,3
%A A193385 _Michael Somos_, Jul 24 2011