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%I A189239 #12 Apr 25 2016 11:45:32
%S A189239 1,1,3,13,77,521,4237,38879,402537,4605697,57796601,787755255,
%T A189239 11583272461,182651526513,3072748617317,54914056549231,
%U A189239 1038486405418449,20713226786502529,434426374539131761,9555736871169618407,219912659890141260661,5283756963089094382705
%N A189239 E.g.f. exp(x/cos(x)*exp(x/cos(x)))
%F A189239 a(n) = n! * sum(r=1..n, ((sum(k=r..n-1, (((-1)^(n-k)+1) * (sum(m=1..n-k, binomial(m+k-1,k-1) * sum(j=1..m, ((sum(i=0..floor((j-1)/2, (j-2*i)^(n-k) * binomial(j,i)))) * binomial(m,j) * (-1)^((n-k)/2-j))/2^j))) * r^(k-r))/((n-k)!*(k-r)!)))+r^(n-r)/(n-r)!)/r!);
%t A189239 With[{nn=30},CoefficientList[Series[Exp[x/Cos[x] Exp[x/Cos[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 08 2015 *)
%o A189239 (Maxima)
%o A189239 a(n):=n!*sum(((sum((((-1)^(n-k)+1)*(sum(binomial(m+k-1,k-1)*sum(((sum((j-2*i)^(n-k)*binomial(j,i),i,0,floor((j-1)/2)))*binomial(m,j)*(-1)^((n-k)/2-j))/2^j,j,1,m),m,1,n-k))*r^(k-r))/((n-k)!*(k-r)!),k,r,n-1))+r^(n-r)/(n-r)!)/r!,r,1,n);
%o A189239 (PARI) x='x+O('x^66); /* that many terms */
%o A189239 egf=exp(x/cos(x)*exp(x/cos(x))); /* = 1 + x + 3/2*x^2 + 13/6*x^3 +... */
%o A189239 Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */
%K A189239 nonn
%O A189239 0,3
%A A189239 _Vladimir Kruchinin_, Apr 19 2011

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