cp's OEIS Frontend

A226838 E.g.f.: exp( Sum_{n>=1} x^(n^2) / n^n ).

%I A226838 #14 Jun 20 2013 21:05:34
%S A226838 1,1,1,1,7,31,91,211,1681,25537,192361,949081,4830871,85109311,
%T A226838 951416467,6696998491,119863554721,2004272484481,25344895874641,
%U A226838 237953743909297,4116426696101671,65285723209356511,903886886890585291,10132514132979331171,165368713321379497777,9835535504812487849281
%N A226838 E.g.f.: exp( Sum_{n>=1} x^(n^2) / n^n ).
%C A226838 E.g.f. may be written as: exp( Sum_{n>=1} ( x^n/n )^n ).
%C A226838 Sum_{n>=0} a(n)/n! = exp( Sum_{n>=1} 1/n^n ) = 3.63746131381110156231...
%F A226838 a(n) == 1 (mod 6) (conjecture - valid up to n=1024; if true for n>=0, why?).
%e A226838 E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 7*x^4/4! + 31*x^5/5! + 91*x^6/6! +...
%e A226838 where
%e A226838 log(A(x)) = x + x^4/2^2 + x^9/3^3 + x^16/4^4 + x^25/5^5 + x^36/6^6 + x^49/7^7 +...
%o A226838 (PARI) {a(n)=n!*polcoeff(exp(sum(m=1,n,(x^m/m)^m)+x*O(x^n)),n)}
%o A226838 for(n=0,30,print1(a(n),", "))
%Y A226838 Cf. A226839, A226890.
%K A226838 nonn
%O A226838 0,5
%A A226838 _Paul D. Hanna_, Jun 19 2013