A274265 - OEIS

%I #10 Sep 08 2022 08:46:17

%S 1,5,64,1331,38416,1419857,64000000,3404825447,208827064576,

%T 14507145975869,1125899906842624,96549157373046875,

%U 9065737908494995456,925103102315013629321,101938319743841411792896,12063348350820368238715343,1525878906250000000000000000

%N a(n) = (3*n - 1)^(n-1).

%C Compare with A052752.

%F 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.

%F A(x) = series reversion( (1 - x)^3*log(1/(1 - x)) ). See A274266.

%F 1 - A(x) = exp(-x/(1 - A(x))^3) = exp(-x/(exp(-3*x/(exp(-3*x/ ...))))).

%F 1 - A(-x*exp(3*x)) = exp(x) = 1/(1 - A(x*exp(-3*x))).

%F 1/(1 - A(x)) = Sum_{n >= 0} (3*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052752.

%p A274265 := n -> (3*n - 1)^(n-1):

%p seq(A274265(n), n = 1..20);

%t Table[(3*n-1)^(n-1), {n,1,25}] (* _G. C. Greubel_, Jun 19 2016 *)

%o (Magma) [(3*n-1)^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Jun 20 2016

%Y Cf. A000169, A052752, A085527, A274266, A274267, A274269.

%K nonn,easy

%O 1,2

%A _Peter Bala_, Jun 19 2016