login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A160617
Numerator of Laguerre(n, -1).
4
1, 2, 7, 17, 209, 773, 13327, 65461, 1441729, 1255151, 234662231, 1702678841, 53334454417, 448162154317, 16083557845279, 13946689584823, 126523856174033, 66120494322107921, 269906478537389909, 34987413853951524577
OFFSET
0,2
LINKS
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
MATHEMATICA
Numerator[Table[LaguerreL[n, -1], {n, 0, 50}]] (* G. C. Greubel, May 06 2018 *)
PROG
(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
(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 */
(Magma) [Numerator((&+[Binomial(n, k)*(1/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018
CROSSREFS
For denominators see A160618.
Cf. A002720.
Sequence in context: A285810 A028888 A082627 * A279334 A283957 A013062
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 14 2009
STATUS
approved