A173044 Product plus sum of five consecutive nonnegative numbers.

10, 135, 740, 2545, 6750, 15155, 30280, 55485, 95090, 154495, 240300, 360425, 524230, 742635, 1028240, 1395445, 1860570, 2441975, 3160180, 4037985, 5100590, 6375715, 7893720, 9687725, 11793730, 14250735, 17100860, 20389465, 24165270, 28480475, 33390880, 38956005

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Nov 21 2010

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A028387, A054602, A166941.

Programs

Magma

[(n+2)*(n^4 +8*n^3 +19*n^2 +12*n +5): n in [0..40]]; // G. C. Greubel, Feb 19 2021

Maple

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

Mathematica

a[n_]:= n*(n+1)*(n+2)*(n+3)*(n+4) + n + (n+1)+(n+2)+(n+3)+(n+4);
Table[a[n],{n,0,5!}]

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

Formula

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4) +n +(n+1) +(n+2) +(n+3) +(n+4).

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

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

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

Extensions

Offset corrected by G. C. Greubel, Feb 19 2021