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A173044 Product plus sum of five consecutive nonnegative numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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

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!}]

PROG

(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

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

CROSSREFS

Cf. A028387, A054602, A166941.

Sequence in context: A324421 A284162 A066156 * A218440 A048666 A114936

Adjacent sequences:  A173041 A173042 A173043 * A173045 A173046 A173047

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Nov 21 2010

EXTENSIONS

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

STATUS

approved

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Last modified May 6 03:25 EDT 2021. Contains 343580 sequences. (Running on oeis4.)