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%I #7 Jul 28 2021 17:01:30
%S 1,1,3,13,109,1041,14191,236293,4712793,113061889,3149562331,
%T 100617526461,3660463878853,149772851618833,6831434952176199,
%U 345197855050549621,19198332224485686961,1168264651674879727233
%N E.g.f.: Sum_{n>=0} (1+x)^(n^2)*x^n/n!.
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 109*x^4/4! +...
%e A(x) = 1 + (1+x)*x + (1+x)^4*x^2/2! + (1+x)^9*x^3/3! + (1+x)^16*x^4/4! +...
%t With[{nn=20},CoefficientList[Series[Sum[(1+x)^n^2 x^n/n!,{n,0,nn}],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 28 2021 *)
%o (PARI) {a(n)=n!*polcoeff(sum(m=0,n,x^m*(1+x+x*O(x^n))^(m^2)/m!),n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 12 2011
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