A082045 - OEIS

%I #11 Dec 24 2022 19:02:55

%S 1,2,6,20,59,150,336,680,1269,2218,3674,5820,8879,13118,18852,26448,

%T 36329,48978,64942,84836,109347,139238,175352,218616,270045,330746,

%U 401922,484876,581015,691854,819020,964256,1129425,1316514,1527638

%N Diagonal sums of number array A082043.

%H G. C. Greubel, <a href="/A082045/b082045.txt">Table of n, a(n) for n = 0..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 a(n) = (n^5+10*n^3+19*n+30)/30.

%F G.f.: (1-4*x+9*x^2-6*x^3+4*x^4)/(1-x)^6. - _R. J. Mathar_, Oct 29 2014

%F E.g.f.: (1/30)*(30 +30*x +45*x^2 +35*x^3 +10*x^4 +x^5)*exp(x). - _G. C. Greubel_, Dec 24 2022

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,2,6,20,59,150},41] (* _Harvey P. Dale_, Mar 18 2018 *)

%o (Magma) [(n^5+10*n^3+19*n+30)/30: n in [0..40]]; // _G. C. Greubel_, Dec 24 2022

%o (SageMath) [(n^5+10*n^3+19*n+30)/30 for n in range(41)] # _G. C. Greubel_, Dec 24 2022

%Y Cf. A082043, A082047.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 03 2003