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%I #14 Sep 21 2016 11:46:29
%S 1,1,1,7,25,181,1201,5251,57457,469225,4340161,50118751,412902601,
%T 5544552157,69259632625,816044592091,12518563864801,152563427413201,
%U 2401979910598657,39326158638385975,575414895837696121
%N E.g.f. exp(x+x^3+x^5)
%H Vincenzo Librandi, <a href="/A191237/b191237.txt">Table of n, a(n) for n = 0..125</a>
%F a(n)=n!*sum(k=1..n, ((-1)^(n-k)+1)*sum(binomial(j,(n-k)/2-j)*binomial(k,j),j,0,k)/(2*k!)), n>0, a(0)=1.
%t a[n_] := n!*Sum[((-1)^(n - k) + 1)* Sum[ Binomial[j, (n - k)/2 - j]*Binomial[k, j], {j, 0, k}]/(2*k!), {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 21 2013 *)
%t With[{nn=20},CoefficientList[Series[Exp[x+x^3+x^5],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 21 2016 *)
%o (Maxima)
%o a(n):=n!*sum(((-1)^(n-k)+1)*sum(binomial(j,(n-k)/2-j)*binomial(k,j),j,0,k)/(2*k!),k,1,n);
%o (PARI) x='x+O('x^66); /* that many terms */
%o Vec(serlaplace(exp(x+x^3+x^5))) /* show terms */ /* Joerg Arndt, May 28 2011 */
%K nonn
%O 0,4
%A _Vladimir Kruchinin_, May 27 2011
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