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%I
%S 1,2,6,28,120,726,4424,31928,249984,2131690,20027392,199240020,
%T 2162269824,24676708798,302660939520,3897794538864,53264941301760,
%U 763279034957010,11499327153704960,181271619624350860
%N E.g.f. x/cos(x)*exp(x/cos(x))
%C A(x)=A009843(x)*exp(A009843(x)).
%H Vincenzo Librandi, <a href="/A189238/b189238.txt">Table of n, a(n) for n = 1..100</a>
%F a(n)=sum(k=1..n-1, binomial(n,k)*k*(1+(-1)^(n-k))*sum(j=1..m, sum(i=0..floor((j-1)/2), binomial(m,j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j,i)*(j-2*i)^(n-k)))*binomial(k+m-1,k-1),m,1,n-k))+n.
%o (Maxima)
%o a(n):=sum(binomial(n,k)*k*(1+(-1)^(n-k))*sum(sum(binomial(m,j)/2^(j)*sum((-1)^((n-k)/2-j)*binomial(j,i)*(j-2*i)^(n-k),i,0,floor((j-1)/2)),j,1,m)*binomial(k+m-1,k-1),m,1,n-k),k,1,n-1)+n;
%o (PARI) x='x+O('x^66); /* that many terms */
%o egf=x/cos(x)*exp(x/cos(x)); /* = x + x^2 + x^3 + 7/6*x^4 + x^5 + 121/120*x^6+ ... */
%o Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */
%K nonn
%O 1,2
%A _Vladimir Kruchinin_, Apr 19 2011
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