cp's OEIS Frontend

A303289 E.g.f. A(x) satisfies: e = Sum_{n>=0} (1/n!) * (1+x)^(n^2) / A(x)^n.

%I A303289 #9 Apr 23 2018 18:31:26
%S A303289 1,2,5,31,390,7926,229448,8769552,421254088,24578690456,1699003652752,
%T A303289 136526757080176,12565047627623648,1308650039442105504,
%U A303289 152723805589647826368,19806995417441865105472,2834647872410303847945600,444947841160313990957842304,76198407065481146373641422336,14170329519388795065500512696832
%N A303289 E.g.f. A(x) satisfies: e = Sum_{n>=0} (1/n!) * (1+x)^(n^2) / A(x)^n.
%H A303289 Paul D. Hanna, <a href="/A303289/b303289.txt">Table of n, a(n) for n = 0..171</a>
%e A303289 E.g.f.: A(x) = 1 + 2*x + 5*x^2/2! + 31*x^3/3! + 390*x^4/4! + 7926*x^5/5! + 229448*x^6/6! + 8769552*x^7/7! + 421254088*x^8/8! + 24578690456*x^9/9! + 1699003652752*x^10/10! + ...
%e A303289 such that A = A(x) satisfies:
%e A303289 e = 1 + (1+x)/A + (1+x)^4/(2!*A^2) + (1+x)^9/(3!*A^3) + (1+x)^16/(4!*A^4) + (1+x)^25/(5!*A^5) + (1+x)^36/(6!*A^6) + (1+x)^49/(7!*A^7) + ...
%o A303289 (PARI) \p100; N=20;
%o A303289 A=[1]; for(i=1,N, A=concat(A,0); A[#A] = Vec( round( sum(n=0,200 + 2*#A, (1+x +x*O(x^#A))^(n^2)/Ser(A)^n/n!*1. )/exp(1)*(#A-1)! ) )[#A]/(#A-1)! ); Vec(serlaplace(Ser(A)))
%Y A303289 Cf. A303290, A303291, A303292.
%K A303289 nonn
%O A303289 0,2
%A A303289 _Paul D. Hanna_, Apr 23 2018