%I #19 Feb 19 2021 18:32:46
%S 10,135,740,2545,6750,15155,30280,55485,95090,154495,240300,360425,
%T 524230,742635,1028240,1395445,1860570,2441975,3160180,4037985,
%U 5100590,6375715,7893720,9687725,11793730,14250735,17100860,20389465,24165270,28480475,33390880,38956005
%N Product plus sum of five consecutive nonnegative numbers.
%H G. C. Greubel, <a href="/A173044/b173044.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = n*(n+1)*(n+2)*(n+3)*(n+4) +n +(n+1) +(n+2) +(n+3) +(n+4).
%F G.f.: 5*(2 +15*x +16*x^2 -14*x^3 +6*x^4 -x^5)/(1-x)^6. - _Colin Barker_, Jun 25 2012
%F a(n) = (n+2)*(n^4 +8*n^3 +19*n^2 +12*n +5) = n^5 +10*n^4 +35*n^3 +50*n^2 +29*n +10. - _Bruno Berselli_, Jun 25 2012
%F E.g.f.: (10 +125*x +240*x^2 +120*x^3 +20*x^4 +x^5)*exp(x). - _G. C. Greubel_, Feb 19 2021
%p A173044:= n-> (n+2)*(n^4 +8*n^3 +19*n^2 +12*n +5); seq(A173044(n), n=0..40) # _G. C. Greubel_, Feb 19 2021
%t a[n_]:= n*(n+1)*(n+2)*(n+3)*(n+4) + n + (n+1)+(n+2)+(n+3)+(n+4);
%t Table[a[n],{n,0,5!}]
%o (Sage) [(n+2)*(n^4 +8*n^3 +19*n^2 +12*n +5) for n in (0..40)] # _G. C. Greubel_, Feb 19 2021
%o (Magma) [(n+2)*(n^4 +8*n^3 +19*n^2 +12*n +5): n in [0..40]]; // _G. C. Greubel_, Feb 19 2021
%Y Cf. A028387, A054602, A166941.
%K nonn,easy
%O 0,1
%A _Vladimir Joseph Stephan Orlovsky_, Nov 21 2010
%E Offset corrected by _G. C. Greubel_, Feb 19 2021