%I A084261
%S A084261 1,1,2,4,9,21,52,134,361,1009,2926,8768,27121,86373,282864,950866,
%T A084261 3277169,11564353,41739130,153919324,579411641,2224535125,8703993420,
%U A084261 34681783422,140637608089,580019801201,2431509498406,10355296410712
%N A084261 A binomial transform of factorial numbers.
%C A084261 Binomial transform of A000142 (with interpolated zeros).
%F A084261 a(n)=sum{k=0..floor(n/2), C(n, 2k)k! }; a(n)=sum{k=0..n, C(n, k)(k/2)!(1+(-1)^k)/
               2 }.
%F A084261 E.g.f.: exp(x)*(1+sqrt(Pi)/2*x*exp(x^2/4)*erf(x/2)). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Sep 25 2003
%F A084261 O.g.f.: A(x) = 1/(1-x-x^2/(1-x-x^2/(1-x-2*x^2/(1-x-2*x^2/(1-x-3*x^2/(1-... 
               -x-[(n+1)/2]*x^2/(1- ...))))))) (continued fraction). - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Jan 17 2006
%F A084261 a_n ~ (1/2) * sqrt(Pi*n/e)*(n/2)^(n/2)*exp(-n/2 + sqrt(2n)). - Cecil 
               C Rousseau (ccrousse(AT)memphis.edu), Mar 14 2006: (cf. A002896).
%Y A084261 Sequence in context: A148071 A000636 A136753 this_sequence A063026 A106219 
               A032129
%Y A084261 Adjacent sequences: A084258 A084259 A084260 this_sequence A084262 A084263 
               A084264
%K A084261 easy,nonn
%O A084261 0,3
%A A084261 Paul Barry (pbarry(AT)wit.ie), May 26 2003