%I #3 Jun 20 2015 20:57:53
%S 1,5,19,89,377,2225,10577,93665,663617,5100545,76194977,612260225,
%T 6223839617,118553476865,1339060610177,13661081703425,312123334199297,
%U 3897935011677185,87368492659073537,1400293336853714945,12252801722806859777,556540136476601135105,15342689556084969711617
%N E.g.f.: Sum_{n>=0} x^n * (1 + x^n)^n * exp(4*x^(n+1)) / n!.
%F E.g.f.: Sum_{n>=0} x^n * (4 + x^n)^n * exp(x^(n+1)) / n!.
%e E.g.f.: A(x) = 1 + 5*x + 19*x^2/2! + 89*x^3/3! + 377*x^4/4! + 2225*x^5/5! +...
%e where
%e A(x) = exp(4*x) + x*(1+x)*exp(4*x^2) + x^2*(1+x^2)^2*exp(4*x^3)/2! + x^3*(1+x^3)^3*exp(4*x^4)/3! + x^4*(1+x^4)^4*exp(4*x^5)/4! + x^5*(1+x^5)^5*exp(4*x^6)/5! +...
%e also
%e A(x) = exp(x) + x*(4+x)*exp(x^2) + x^2*(4+x^2)^2*exp(x^3)/2! + x^3*(4+x^3)^3*exp(x^4)/3! + x^4*(4+x^4)^4*exp(x^5)/4! + x^5*(4+x^5)^5*exp(x^6)/5! +...
%o (PARI) {a(n) = local(A=1); A = sum(m=0,n,x^m/m!*(1 + x^m +x*O(x^n))^m * exp(4*x^(m+1) +x*O(x^n))); n!*polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%o (PARI) {a(n) = local(A=1); A = sum(m=0,n,x^m/m!*(4 + x^m +x*O(x^n))^m * exp(x^(m+1) +x*O(x^n))); n!*polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A259202, A259203, A259205.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 20 2015
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