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%I #9 Jul 26 2016 20:43:58
%S 0,1,16,71,205,470,931,1666,2766,4335,6490,9361,13091,17836,23765,
%T 31060,39916,50541,63156,77995,95305,115346,138391,164726,194650,
%U 228475,266526,309141,356671,409480,467945,532456,603416,681241,766360,859215,960261,1069966
%N a(n) = n*(n + 1)*(13*n^2 + 13*n - 14)/24.
%C Partial sum of сentered 13-gonal (or tridecagonal) pyramidal numbers.
%C This is the case k=13 of the formula n*(n + 1)*(k*n^2 + k*n - 2*k + 12)/24.
%H OEIS Wiki, <a href="https://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: x*(1 + 11*x + x^2)/(1 - x)^5.
%F a(n) = Sum_{k = 0..n} A062025(k).
%t Table[n (n + 1) (13 n^2 + 13 n - 14)/24, {n, 0, 50}]
%o (PARI) a(n)=n*(n+1)*(13*n^2+13*n-14)/24 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y Cf. A062025.
%Y Cf. similar sequences listed in A264854.
%K nonn,easy
%O 0,3
%A _Ilya Gutkovskiy_, Nov 27 2015
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