OFFSET
1,2
COMMENTS
Compare with A052752.
FORMULA
E.g.f. A(x) = 1 - exp(-1/3*T(3*x)) = x + 5*x^2/2! + 8^2*x^3/3! + 11^3*x^4/4! + 14^4*x^5/5! + ..., where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
A(x) = series reversion( (1 - x)^3*log(1/(1 - x)) ). See A274266.
1 - A(x) = exp(-x/(1 - A(x))^3) = exp(-x/(exp(-3*x/(exp(-3*x/ ...))))).
1 - A(-x*exp(3*x)) = exp(x) = 1/(1 - A(x*exp(-3*x))).
1/(1 - A(x)) = Sum_{n >= 0} (3*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052752.
MATHEMATICA
Table[(3*n-1)^(n-1), {n, 1, 25}] (* G. C. Greubel, Jun 19 2016 *)
PROG
(Magma) [(3*n-1)^(n-1): n in [1..20]]; // Vincenzo Librandi, Jun 20 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Jun 19 2016
STATUS
approved