A244883 - OEIS

%I #19 Sep 08 2022 08:46:08

%S 1,14,100,472,1691,4988,12744,29160,61149,119482,220220,386464,650455,

%T 1056056,1661648,2543472,3799449,5553510,7960468,11211464,15540019,

%U 21228724,28616600,38107160,50177205,65386386,84387564,107938000,136911407,172310896,215282848

%N Expansion of (1+6*x+16*x^2+8*x^3+x^4)/(1-x)^8.

%H Todd Silvestri, <a href="/A244883/b244883.txt">Table of n, a(n) for n = 0..10000</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = ((n+1)*(n+2)*(n+3)*(n*(n+4)*(n*(16*n+57)+137)+420))/2520. - _Todd Silvestri_, Nov 16 2014

%t a[n_Integer/;n>=0]:=((n+1) (n+2) (n+3) (n (n+4) (n (16 n+57)+137)+420))/2520 (* _Todd Silvestri_, Nov 16 2014 *)

%t CoefficientList[Series[(1 + 6 x + 16 x^2 + 8 x^3 + x^4) / (1 - x)^8, {x, 0, 100}], x] (* _Vincenzo Librandi_, Nov 16 2014 *)

%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,14,100,472,1691,4988,12744,29160},40] (* _Harvey P. Dale_, May 11 2020 *)

%o (Magma) [((n+1)*(n+2)*(n+3)*(n*(n+4)*(n*(16*n+57)+137)+420))/2520: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2014

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 08 2014