A055811 - OEIS

%I #13 Oct 21 2022 21:37:19

%S 1,63,192,432,832,1452,2364,3653,5418,7773,10848,14790,19764,25954,

%T 33564,42819,53966,67275,83040,101580,123240,148392,177436,210801,

%U 248946,292361,341568,397122,459612,529662

%N a(n) = T(n,n-6), array T as in A055807.

%H G. C. Greubel, <a href="/A055811/b055811.txt">Table of n, a(n) for n = 6..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 From _G. C. Greubel_, Jan 23 2020: (Start)

%F a(n) = n*(1584 - 310*n - 85*n^2 + 10*n^3 + n^4)/120 for n > 6, with a(6) = 1.

%F G.f.: x^6*(1 + 57*x - 171*x^2 + 205*x^3 - 125*x^4 + 39*x^5 - 5*x^6)/(1-x)^6.

%F E.g.f.: (-1)*x*(7200 +4320*x +720*x^2 -120*x^3 -54*x^4 +5*x^5 - (7200 -2880*x + 120*x^3 + 6*x^4)*exp(x))/720. (End)

%p seq( `if`(n=6, 1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120), n=6..30); # _G. C. Greubel_, Jan 23 2020

%t Table[If[n==6,1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120], {n,6,30}] (* _G. C. Greubel_, Jan 23 2020 *)

%o (PARI) vector(25, n, my(m=n+5); if(m==6,1, m*(1584 -310*m -85*m^2 +10*m^3 +m^4)/120) ) \\ _G. C. Greubel_, Jan 23 2020

%o (Magma) [1] cat [n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120: n in [7.30]]; // _G. C. Greubel_, Jan 23 2020

%o (Sage) [1]+[n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 for n in (7..30)] # _G. C. Greubel_, Jan 23 2020

%o (GAP) Concatenation([1], List([7..30], n-> n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 )); # _G. C. Greubel_, Jan 23 2020

%Y Cf. A055807, A055809, A055810, A055815, A055816, A055817.

%K nonn,easy

%O 6,2

%A _Clark Kimberling_, May 28 2000