Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #25 Feb 02 2023 05:04:18
%S 3,2,6,12,72,240,2160,10080,120960,725760,10886400,79833600,
%T 1437004800,12454041600,261534873600,2615348736000,62768369664000,
%U 711374856192000,19207121117184000,243290200817664000,7298706024529920000,102181884343418880000,3372002183332823040000
%N Expansion of e.g.f. (3+2*x)/(1-x^2).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=561">Encyclopedia of Combinatorial Structures 561</a>.
%F E.g.f.: (2*x+3)/(1-x^2).
%F Recurrence: {a(1)=2, a(0)=3, (-2-n^2-3*n)*a(n) + a(n+2) = 0}.
%F a(n) = Sum(1/2*(3*_alpha+2)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^2))*n!.
%F a(n) = 3n! if n is even, 2n! otherwise.
%F a(n) = n!*A176059(n). - _R. J. Mathar_, Jun 03 2022
%F Sum_{n>=0} 1/a(n) = (5*e^2-1)/(12*e) = cosh(1)/3 + sinh(1)/2. - _Amiram Eldar_, Feb 02 2023
%p spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Prod(Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=30},CoefficientList[Series[(3+2x)/(1-x^2),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Dec 12 2021 *)
%Y Cf. A176059.
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000