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A325061 E.g.f. A(x) satisfies: x = Sum_{n>=1} x^n * exp(n^2*x) / A(x)^n. 0

%I

%S 1,2,7,40,397,6206,141139,4319428,168516121,8074235962,462150372511,

%T 30961663872800,2389485847199653,209753391483063286,

%U 20726915554125563371,2285734324175430121276,279253590786131032786993,37559078525515696049196914,5530800506305098048787614007,887392909503840580659865765144,154464699454782791251249780648381

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

%e E.g.f.: A(x) = 1 + 2*x + 7*x^2/2! + 40*x^3/3! + 397*x^4/4! + 6206*x^5/5! + 141139*x^6/6! + 4319428*x^7/7! + 168516121*x^8/8! + 8074235962*x^9/9! + 462150372511*x^10/10! + ...

%e such that

%e x = x*exp(x)/A(x) + x^2*exp(2^2*x)/A(x)^2 + x^3*exp(3^2*x)/A(x)^3 + x^4*exp(4^2*x)/A(x)^4 + x^5*exp(5^2*x)/A(x)^5 + x^6*exp(6^2*x)/A(x)^6 + ...

%e RELATED SERIES.

%e log(A(x)) = 2*x + 3*x^2/2! + 14*x^3/3! + 170*x^4/4! + 2984*x^5/5! + 75432*x^6/6! + 2487568*x^7/7! + 102634576*x^8/8! + 5137520256*x^9/9! + ...

%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A = concat(A,0);

%o A[#A] = polcoeff( sum(m=1,#A, x^m * exp(m^2*x +O(x^(n+2))) / Ser(A)^m), #A)); n!*A[n+1]}

%o for(n=0,30, print1(a(n),", "))

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 12 2019

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)