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A160617 Numerator of Laguerre(n, -1).

%I A160617 #21 Sep 08 2022 08:45:45
%S A160617 1,2,7,17,209,773,13327,65461,1441729,1255151,234662231,1702678841,
%T A160617 53334454417,448162154317,16083557845279,13946689584823,
%U A160617 126523856174033,66120494322107921,269906478537389909,34987413853951524577
%N A160617 Numerator of Laguerre(n, -1).
%H A160617 G. C. Greubel, <a href="/A160617/b160617.txt">Table of n, a(n) for n = 0..440</a>
%F A160617 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
%t A160617 Numerator[Table[LaguerreL[n, -1], {n, 0, 50}]] (* _G. C. Greubel_, May 06 2018 *)
%o A160617 (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
%o A160617 (PARI) for(n=0,30, print1(numerator(sum(k=0,n, binomial(n,k)*(1/k!))), ", ")) \\ _G. C. Greubel_, May 06 2018
%o A160617 (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));
%o A160617 makelist(num(s(n)),n,0,20); /* _Vladimir Kruchinin_, Sep 30 2016 */
%o A160617 (Magma) [Numerator((&+[Binomial(n,k)*(1/Factorial(k)): k in [0..n]])): n in [0..30]]; // _G. C. Greubel_, May 06 2018
%Y A160617 For denominators see A160618.
%Y A160617 Cf. A002720.
%K A160617 nonn,frac
%O A160617 0,2
%A A160617 _N. J. A. Sloane_, Nov 14 2009