A316567 - OEIS

%I #7 Jul 30 2018 00:37:31

%S 1,2,7,48,613,12678,376635,14843748,736850985,44460709034,

%T 3178138510415,263969177593784,25092912792070221,2697122248172619374,

%U 324551651315721416259,43360400395276940296748,6386567528761097854601681,1030796192558122817118624722,181349613039877947587685266455,34616458231107257107670541291456

%N E.g.f. A(x) satisfies: Sum_{n>=0} 1/n! * exp(n^2*x)/A(x)^n = exp(1).

%H Paul D. Hanna, <a href="/A316567/b316567.txt">Table of n, a(n) for n = 0..70</a>

%e E.g.f.: A(x) = 1 + 2*x + 7*x^2/2! + 48*x^3/3! + 613*x^4/4! + 12678*x^5/5! + 376635*x^6/6! + 14843748*x^7/7! + 736850985*x^8/8! + 44460709034*x^9/9! + 3178138510415*x^10/10! + ...

%e such that

%e e = 1 + exp(x)/A(x) + exp(4*x)/A(x)^2/2! + exp(9*x)/A(x)^3/3! + exp(16*x)/A(x)^4/4! + exp(25*x)/A(x)^5/5! + exp(36*x)/A(x)^6/6! + ... + exp(n^2*x)/A(x)^n/n! + ...

%o (PARI) /* Requires setting appropriate precision and index ranges */

%o {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = round( (#A-1)!*Vec( sum(n=0,400, exp(n^2*x +x*O(x^#A) )/n!/Ser(A)^n*1. )/exp(1) )[#A])/(#A-1)! ); n!*A[n+1]}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A316986.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 06 2018