A274267 a(n) = (4*n - 1)^(n-1).

1, 7, 121, 3375, 130321, 6436343, 387420489, 27512614111, 2251875390625, 208728361158759, 21611482313284249, 2472159215084012303, 309629344375621415601, 42141982597572021484375, 6193386212891813387462761, 977480813971145474830595007, 164890958756244164895763202881

Offset: 1

Author

Peter Bala, Jun 19 2016

Keywords

• nonn
• easy

Comments

Compare with A052774.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..321

Crossrefs

Cf. A000169, A052774, A274265, A274266, A274268, A274269.

Programs

Magma

[(4*n-1)^(n-1): n in [1..25]]; // Vincenzo Librandi, Jun 20 2016

Maple

A274267 := n -> (4*n - 1)^(n-1):
seq(A274267(n), n = 1..20);

Mathematica

Table[(4*n-1)^(n-1), {n,1,25}] (* G. C. Greubel, Jun 19 2016 *)

PARI

for(n=1,30, print1((4*n-1)^(n-1), ", ")) \\ G. C. Greubel, Nov 16 2017

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.