A160621 Numerator of Laguerre(n, 1).
1, 0, -1, -2, -5, -7, -37, -17, 887, 1405, 168919, 958271, 3086837, 122693929, 559876951, 15779421743, 337767590383, 1531923385313, 11912361112367, -6819537030283, -21032925955607701, -313699426574980519, -16703816669710968821, -212752402370938916881
Offset: 0
Examples
1, 0, -1/2, -2/3, -5/8, -7/15, -37/144, -17/420, 887/5760, 1405/4536, 168919/403200, 958271/1995840, ... = A160621/A160622.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450
Programs
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Magma
[Numerator((&+[Binomial(n,k)*((-1)^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018
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Mathematica
Numerator/@LaguerreL[Range[0,30],1] (* Harvey P. Dale, May 01 2011 *)
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PARI
for(n=0,30, print1(numerator(sum(k=0,n, binomial(n,k)*((-1)^k/k!))), ", ")) \\ G. C. Greubel, May 06 2018
Formula
Numerators of coefficients in expansion of exp(-x/(1 - x))/(1 - x). - Ilya Gutkovskiy, Aug 29 2018