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a(n) = T(n,n-5), array T as in A055807.
8

%I #18 Oct 21 2022 21:04:36

%S 1,31,80,160,280,450,681,985,1375,1865,2470,3206,4090,5140,6375,7815,

%T 9481,11395,13580,16060,18860,22006,25525,29445,33795,38605,43906,

%U 49730,56110,63080,70675,78931,87885,97575

%N a(n) = T(n,n-5), array T as in A055807.

%H G. C. Greubel, <a href="/A055810/b055810.txt">Table of n, a(n) for n = 5..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: x^5*(1 +26*x -65*x^2 +60*x^3 -25*x^4 +4*x^5)/(1-x)^5. - _Colin Barker_, Feb 22 2012

%F From _G. C. Greubel_, Jan 23 2020: (Start)

%F a(n) = (240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n > 5, with a(5) = 1.

%F E.g.f.: (-1200 -720*x +100*x^3 +25*x^4 -4*x^5 + (1200 -480*x -120*x^2 +60*x^3 +5*x^4)*exp(x))/120. (End)

%p seq( `if`(n=5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24), n=5..40); # _G. C. Greubel_, Jan 23 2020

%t Table[If[n==5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24], {n,5,40}] (* _G. C. Greubel_, Jan 23 2020 *)

%o (PARI) vector(40, n, my(m=n+4); if(m==5, 1, (240 -54*m -49*m^2 +6*m^3 +m^4)/24)) \\ _G. C. Greubel_, Jan 23 2020

%o (Magma) [1] cat [(240 -54*n -49*n^2 +6*n^3 +n^4)/24: n in [6..40]]; // _G. C. Greubel_, Jan 23 2020

%o (Sage) [1]+[(240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n in (6..40)] # _G. C. Greubel_, Jan 23 2020

%o (GAP) Concatenation([1], List([6..40], n-> (240 -54*n -49*n^2 +6*n^3 +n^4)/24 )); # _G. C. Greubel_, Jan 23 2020

%Y Cf. A055807, A055809, A055811, A055815, A055816, A055817.

%K nonn,easy

%O 5,2

%A _Clark Kimberling_, May 28 2000