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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

Crossrefs

Cf. A036503 (denominators).

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

Programs

Magma

[Numerator(n^(n-1)/Factorial(n)): n in [1..30]]; // G. C. Greubel, Sep 09 2018

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 *)

PARI

for(n=1, 30, print1(numerator(n^(n-1)/n!), ", ")) \\ G. C. Greubel, Sep 09 2018

Sage

[numerator(n^(n-1)/factorial(n)) for n in (1..30)] # G. C. Greubel, Feb 08 2019