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%I #8 Nov 17 2024 09:53:00
%S 0,1,22,153,624,1875,4626,9947,19328,34749,58750,94501,145872,217503,
%T 314874,444375,613376,830297,1104678,1447249,1870000,2386251,3010722,
%U 3759603,4650624,5703125,6938126,8378397,10048528,11974999,14186250,16712751,19587072
%N (7*n^5+5*n^3)/12.
%C 7*n^5+5*n^3 = 0 (mod.12) for all n.
%H Vincenzo Librandi, <a href="/A245380/b245380.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: x*(x^4 + 16*x^3 + 36*x^2 + 16*x + 1)/(x - 1)^6.
%t Table[(7 n^5 + 5 n^3)/12, {n, 0, 40}] (* or *) CoefficientList[Series[x (x^4 + 16 x^3 + 36 x^2 + 16 x + 1)/(x - 1)^6, {x, 0, 40}], x]
%o (Magma) [(7*n^5+5*n^3)/12: n in [0..40]];
%K nonn,easy
%O 0,3
%A _Vincenzo Librandi_, Jul 20 2014