A036504 -id:A036504 - cp's OEIS frontend

A036503 Denominator of n^(n-2)/n!.

1, 2, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, 479001600, 868725, 14350336, 638512875, 20922789888000, 14889875, 6402373705728000, 14849255421, 7567605760000, 17717861581875, 1124000727777607680000, 2505147019375

Offset: 1

N. J. A. Sloane

Denominators 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

Absolute value of denominator of the coefficient of 1/(n*x-1) in the partial fraction decomposition of 1/(x-1)*1/(2*x-1)*...*1/(n*x-1). [Joris Roos (jorisr(AT)gmx.de), Aug 02 2009]

			1, 1/2, 1/2, 2/3, 25/24, 9/5, 2401/720, 2048/315, 59049/4480, 15625/567, 214358881/3628800, ...

G. C. Greubel, Table of n, a(n) for n = 1..450

Cf. A036502, A036504.

[Denominator(n^(n - 2)/Factorial(n)): n in [1..50]]; // G. C. Greubel, Nov 14 2017

Denominator[Table[n^(n - 2)/n!, {n, 1, 50}]] (* G. C. Greubel, Nov 14 2017 *)

for(n=1, 50, print1(denominator(n^(n-2)/n!), ", ")) \\ G. C. Greubel, Nov 14 2017

A227831 Numerators of coefficients in Taylor series for LambertW(x).

Original entry on oeis.org

0, 1, -1, 3, -8, 125, -54, 16807, -16384, 531441, -156250, 2357947691, -2985984, 1792160394037, -7909306972, 320361328125, -35184372088832, 2862423051509815793, -5083731656658, 5480386857784802185939, -32000000000000000, 41209797661291758429, -244636361793658185164

Offset: 0

N. J. A. Sloane, Aug 01 2013

The denominators are 1, 1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, ..., which is A095996 prefixed by 1.

			0, 1, -1, 3/2, -8/3, 125/24, -54/5, 16807/720, -16384/315, 531441/4480, -156250/567, 2357947691/3628800, -2985984/1925, ...

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., Eq. (5.66).
M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 34.

Alois P. Heinz, Table of n, a(n) for n = 0..300
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, On the Lambert W Function
Eric Weisstein's World of Mathematics, Lambert W-Function
Wikipedia, Lambert W function

Cf. A095996. See also A036504/A036503.

series(LambertW(x),x,30); # N. J. A. Sloane, Jan 08 2021

Numerator[CoefficientList[Series[LambertW[x], {x, 0, 22}], x]] (* Mats Granvik, Nov 24 2013 *)
Numerator[CoefficientList[InverseSeries[Series[x/Sum[((-x)^n)/Factorial[n], {n, 0, 22}], {x, 0, 22}]], x]] (* Mats Granvik, Nov 24 2013 *)

Numerators of series reversion of x/(Sum_{n=0..infinity} ((-x)^n)/n!). - Mats Granvik, Nov 24 2013

A036502 Numerator of n^(n-2)/n!.

Original entry on oeis.org

1, 1, 1, 2, 25, 9, 2401, 2048, 59049, 15625, 214358881, 248832, 137858491849, 564950498, 21357421875, 2199023255552, 168377826559400929, 282429536481, 288441413567621167681, 1600000000000000, 1962371317204369449, 11119834626984462962

Offset: 1

N. J. A. Sloane

			1, 1/2, 1/2, 2/3, 25/24, 9/5, 2401/720, 2048/315, 59049/4480, 15625/567, 214358881/3628800, ...

Cf. A036503, A036504.

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A036503 Denominator of n^(n-2)/n!.

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A227831 Numerators of coefficients in Taylor series for LambertW(x).

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A036502 Numerator of n^(n-2)/n!.

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