%I #13 Sep 08 2022 08:45:05

%S 62,602,2702,8162,19502,39962,73502,124802,199262,303002,442862,

%T 626402,861902,1158362,1525502,1973762,2514302,3159002,3920462,

%U 4812002,5847662,7042202,8411102,9970562,11737502,13729562,15965102,18463202

%N First differences of (n+1)^6-n^6 (A022522).

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

%F a(n) = 30*n^4 + 120*n^3 + 210*n^2 + 180*n + 62.

%F G.f.: 2*(31 + 146*x + 156*x^2 + 26*x^3 + x^4)/(1 - x)^5. [_Bruno Berselli_, Feb 25 2015]

%t Differences[Table[(n + 1)^6 - n^6, {n, 0, 30}]] (* _Harvey P. Dale_, Dec 27 2011 *)

%o (Magma) [30*n^4+120*n^3+210*n^2+180*n+62: n in [0..30]]; // _Bruno Berselli_, Feb 25 2015

%Y Cf. A001014, A022522, A069474, A069475, A069476, A068236.

%K nonn,easy

%O 0,1

%A Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 26 2002

%E Offset changed from 1 to 0 and added a(0)=62 by _Bruno Berselli_, Feb 25 2015