A274269 a(n) = (5*n - 1)^(n-1).

1, 9, 196, 6859, 331776, 20511149, 1544804416, 137231006679, 14048223625216, 1628413597910449, 210832519264920576, 30155888444737842659, 4722366482869645213696, 803596764671634487466709, 147653612273582215982104576, 29134419507545592909032289199

Offset: 1

Author

Peter Bala, Jun 19 2016

Keywords

• nonn
• easy

Comments

Compare with A052782.

Crossrefs

Cf. A000169, A052782, A274265, A274267, A274270.

Programs

Magma

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

Maple

A274269 := n -> (5*n - 1)^(n-1):
seq(A274269(n), n = 1..20);

Mathematica

Table[(5*n-1)^(n-1), {n,1,25}] (* G. C. Greubel, Jun 19 2016 *)

Formula

E.g.f. A(x) = 1 - exp(-1/5*T(5*x)) = x + 9*x^2/2! + 14^2*x^3/3! + 19^3*x^4/4! + 24^4*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)^5*log(1/(1 - x)) ). See A274270.

1 - A(x) = exp(-x/(1 - A(x))^5) = exp(-x/(exp(-5*x/(exp(-5*x/ ...))))).

1 - A(-x*exp(5*x)) = exp(x) = 1/(1 - A(x*exp(-5*x))).

1/(1 - A(x)) = Sum_{n >= 0} (5*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052782.