A160617 Numerator of Laguerre(n, -1).

1, 2, 7, 17, 209, 773, 13327, 65461, 1441729, 1255151, 234662231, 1702678841, 53334454417, 448162154317, 16083557845279, 13946689584823, 126523856174033, 66120494322107921, 269906478537389909, 34987413853951524577

Offset: 0

Author

N. J. A. Sloane, Nov 14 2009

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..440

Crossrefs

For denominators see A160618.

Cf. A002720.

Programs

Magma

[Numerator((&+[Binomial(n,k)*(1/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018

Mathematica

Numerator[Table[LaguerreL[n, -1], {n, 0, 50}]] (* G. C. Greubel, May 06 2018 *)

Maxima

s(n):=if n=0 then 1/2 else 1/(n+2)*(n +1 +sum(s(n-i-2)*(i+1), i,0,n-2));
makelist(num(s(n)),n,0,20); /* Vladimir Kruchinin, Sep 30 2016 */

PARI

lista(nn) = {x = 'x + O('x^nn); v = exp(x/(1-x))/(1-x); for (n=0, nn-1, print1(numerator(polcoeff(v, n)), ", "););} \\ Michel Marcus, Nov 27 2015

PARI

for(n=0,30, print1(numerator(sum(k=0,n, binomial(n,k)*(1/k!))), ", ")) \\ G. C. Greubel, May 06 2018

Formula

a(n) = numerator(s(n)), where s(0)=1/2, s(n) = 1/(n+2)*(n +1 + Sum_{i=0..n-2} s(n-i-2)*(i+1)). - Vladimir Kruchinin, Sep 30 2016