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A173044 Product plus sum of five consecutive nonnegative numbers.

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