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A263689 a(n) = (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12.

%I A263689 #44 Jul 22 2016 17:30:00
%S A263689 1,1,2,34,277,1301,4426,12202,29009,61777,120826,220826,381877,630709,
%T A263689 1002002,1539826,2299201,3347777,4767634,6657202,9133301,12333301,
%U A263689 16417402,21571034,28007377,35970001,45735626,57617002,71965909,89176277,109687426,133987426,162616577,196171009,235306402,280741826
%N A263689 a(n) = (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12.
%H A263689 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A263689 G.f.: (1 - 6*x + 16*x^2 + 6*x^3 + 81*x^4 + 20*x^5 + 2*x^6)/(1 - x)^7.
%F A263689 a(n + 1) = a(n) + n^5, a(0) = 1.
%F A263689 a(n + 1) - a(n) = A000584(n).
%F A263689 a(n + 1) = A000539(n) + 1.
%F A263689 Sum_{n>0} 1/(a(n + 1) - a(n)) = zeta(5) = 1.036927755...
%e A263689 a(0) = 1,
%e A263689 a(1) = 0^5 + 1 = 1,
%e A263689 a(2) = 1^5 + 1 = 2,
%e A263689 a(3) = 2^5 + 2 = 34,
%e A263689 a(4) = 3^5 + 34 = 227,
%e A263689 a(5) = 4^5 + 227 = 1301, etc.
%t A263689 Table[(1/12) (12 + (-1 + n)^2 n^2 (-1 + 2 (-1 + n) n)), {n, 0, 35}]
%o A263689 (PARI) first(m)=vector(m,n,n--;(2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12) \\ _Anders Hellström_, Nov 20 2015
%Y A263689 Cf. A000124, A000539, A000584, A056520, A154323.
%K A263689 nonn,easy
%O A263689 0,3
%A A263689 _Ilya Gutkovskiy_, Nov 20 2015