OFFSET
1,2
COMMENTS
Compare with A052774.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..321
FORMULA
E.g.f. A(x) = 1 - exp(-1/4*T(4*x)) = x + 7*x^2/2! + 11^2*x^3/3! + 15^3*x^4/4! + 19^4*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)^4*log(1/(1 - x)) ). See A274268.
1 - A(x) = exp(-x/(1 - A(x))^4) = exp(-x/(exp(-4*x/(exp(-4*x/ ...))))).
1 - A(-x*exp(4*x)) = exp(x) = 1/(1 - A(x*exp(-4*x))).
1/(1 - A(x)) = Sum_{n >= 0} (4*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052774.
MATHEMATICA
Table[(4*n-1)^(n-1), {n, 1, 25}] (* G. C. Greubel, Jun 19 2016 *)
PROG
(Magma) [(4*n-1)^(n-1): n in [1..25]]; // Vincenzo Librandi, Jun 20 2016
(PARI) for(n=1, 30, print1((4*n-1)^(n-1), ", ")) \\ G. C. Greubel, Nov 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Jun 19 2016
STATUS
approved