A036504 Numerator of n^(n-1)/n!.

1, 1, 3, 8, 125, 54, 16807, 16384, 531441, 156250, 2357947691, 2985984, 1792160394037, 7909306972, 320361328125, 35184372088832, 2862423051509815793, 5083731656658, 5480386857784802185939, 32000000000000000, 41209797661291758429

Offset

1,3

Comments

(-1)^(n+1)* n-th numerator of coefficient in LambertW(x) power series, where LambertW(x) is the transcendental function satisfying LambertW(x)*exp( LambertW(x) )=x. - Benoit Cloitre, May 08 2002

Links

G. C. Greubel, Table of n, a(n) for n = 1..250

Mathematica

Numerator[Table[n^(n - 1)/n!, {n, 1, 30}]] (* G. C. Greubel, Sep 09 2018 *)
CoefficientList[-LambertW[-x]/x + O[x]^21, x] // Numerator (* Jean-François Alcover, Jan 15 2019 *)

Prog

(PARI) for(n=1, 30, print1(numerator(n^(n-1)/n!), ", ")) \\ G. C. Greubel, Sep 09 2018
(Magma) [Numerator(n^(n-1)/Factorial(n)): n in [1..30]]; // G. C. Greubel, Sep 09 2018
(SageMath) [numerator(n^(n-1)/factorial(n)) for n in (1..30)] # G. C. Greubel, Feb 08 2019
(Python)
from sympy import factorint
from sympy.ntheory.factor_ import digits
def A036504(n):
    m = n**(n-1)
    for p, e in factorint(n).items():
        m //= p**min(e*(n-1), (n-sum(digits(n, p)[1:]))//(p-1))
    return m # Chai Wah Wu, May 03 2026

Crossrefs

Cf. A036503 (denominators).

A095996 is a better version of the denominators of the LambertW function. - N. J. A. Sloane, Jan 08 2021

Sequence in context: A051047 A192629 A245458 * A227831 A132491 A083112

Adjacent sequences: A036501 A036502 A036503 * A036505 A036506 A036507

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved