%I #22 Sep 08 2022 08:45:59
%S 0,10,50,138,292,530,870,1330,1928,2682,3610,4730,6060,7618,9422,
%T 11490,13840,16490,19458,22762,26420,30450,34870,39698,44952,50650,
%U 56810,63450,70588,78242,86430,95170,104480,114378,124882
%N a(n) = n*(3*n^2 + 6*n + 1).
%D Jolley, Summation of Series, Dover (1961), eq. 45 on page 8.
%H Vincenzo Librandi, <a href="/A196507/b196507.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 2*5 + 5*8 + 8*11 + ... + (3*k-1)*(3*k+2) + ... (n terms) = n*A100536(n+1).
%F G.f.: -2*x*(-5 - 5*x + x^2) / (x-1)^4.
%F E.g.f.: exp (x)*(10*x + 15*x^2 + 3*x^3). - _Franck Maminirina Ramaharo_, Nov 22 2018
%o (Magma) [n*(3*n^2+6*n+1): n in [0..30]]; // _Vincenzo Librandi_, Oct 05 2011
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Oct 03 2011