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

1, 2, 7, 40, 397, 6206, 141139, 4319428, 168516121, 8074235962, 462150372511, 30961663872800, 2389485847199653, 209753391483063286, 20726915554125563371, 2285734324175430121276, 279253590786131032786993, 37559078525515696049196914, 5530800506305098048787614007, 887392909503840580659865765144, 154464699454782791251249780648381

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Example

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! + ...
such that
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 + ...
RELATED SERIES.
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! + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
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]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A130715 A317723 A340005 * A358745 A215207 A106871

Adjacent sequences: A325058 A325059 A325060 * A325062 A325063 A325064

Keyword

nonn

Author

Paul D. Hanna, Apr 12 2019

Status

approved