%I #33 Jun 24 2023 21:52:34
%S 0,1,2,3,4,5,726,5047,20168,60489,151210,332651,665292,1235533,
%T 2162174,3603615,5765776,8910737,13366098,19535059,27907220,39070101,
%U 53721382,72681863,96909144,127512025,165765626,213127227,271252828,342014429
%N a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5).
%H Vincenzo Librandi, <a href="/A001096/b001096.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F G.f.: x*(1 -5*x +10*x^2 -10*x^3 +5*x^4 +719*x^5)/(1-x)^7. - _Ralf Stephan_, Dec 30 2002
%F From _G. C. Greubel_, Aug 26 2019: (Start)
%F a(n) = n + 6!*binomial(n,6).
%F E.g.f.: x*(1 + x^5)*exp(x). (End)
%p seq(n + 6!*binomial(n,6), n=0..35); # _G. C. Greubel_, Aug 26 2019
%t Table[n + 6!*Binomial[n,6], {n,0,35}] (* _G. C. Greubel_, Aug 26 2019 *)
%o (Magma) [n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5): n in [0..35]]; // _Vincenzo Librandi_, Apr 30 2011
%o (PARI) vector(35, n, (n-1) + 6!*binomial(n-1,6)) \\ _G. C. Greubel_, Aug 26 2019
%o (Sage) [n + 720*binomial(n,6) for n in (0..35)] # _G. C. Greubel_, Aug 26 2019
%o (GAP) List([0..35], n-> n + 720*Binomial(n,6)); # _G. C. Greubel_, Aug 26 2019
%Y Equals A053625(n) + n.
%Y Cf. A001094, A001095.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Ray Wills (rwills(AT)vmprofs.estec.esa.nl)
%E More terms from _James A. Sellers_, Sep 19 2000