OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 12 2019
STATUS
approved