A274265 a(n) = (3*n - 1)^(n-1).

1, 5, 64, 1331, 38416, 1419857, 64000000, 3404825447, 208827064576, 14507145975869, 1125899906842624, 96549157373046875, 9065737908494995456, 925103102315013629321, 101938319743841411792896, 12063348350820368238715343, 1525878906250000000000000000

Offset

1,2

Comments

Compare with A052752.

Links

Table of n, a(n) for n=1..17.

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.

Maple

A274265 := n -> (3*n - 1)^(n-1):
seq(A274265(n), n = 1..20);

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

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

Sequence in context: A266095 A255523 A193222 * A073179 A192558 A179156

Adjacent sequences: A274262 A274263 A274264 * A274266 A274267 A274268

Keyword

nonn,easy

Author

Peter Bala, Jun 19 2016

Status

approved