This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A154324 #16 Sep 12 2016 06:21:32
%S A154324 1,1,2,3,6,12,23,43,74,124,195,300,441,637,890,1226,1647,2187,2848,
%T A154324 3673,4664,5874,7305,9021,11024,13390,16121,19306,22947,27147,31908,
%U A154324 37348,43469,50405,58158,66879,76570,87400,99371,112671,127302,143472,161183,180664
%N A154324 Diagonal sums of number triangle A113582.
%H A154324 G. C. Greubel, <a href="/A154324/b154324.txt">Table of n, a(n) for n = 0..1000</a>
%H A154324 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-8,6,6,-8,0,3,-1).
%F A154324 G.f.: (1 -2*x -x^2 +5*x^3 -x^4 -2*x^5 +x^6)/((1-x)*(1-x^2))^3.
%F A154324 a(n) = Sum_{k=0..floor(n/2)} ( 1 + C(k+1,2)*C(n-2k+1,2) ).
%F A154324 From _Colin Barker_, Sep 12 2016: (Start)
%F A154324 a(n) = (2895 + 945*(-1)^n + (1786-90*(-1)^n)*n - 30*(3+(-1)^n)*n^2 + 40*n^3 + 30*n^4 + 4*n^5)/3840.
%F A154324 a(n) = (2*n^5+15*n^4+20*n^3-60*n^2+848*n+1920)/1920 for n even.
%F A154324 a(n) = (2*n^5+15*n^4+20*n^3-30*n^2+938*n+975)/1920 for n odd. (End)
%t A154324 LinearRecurrence[{3,0,-8,6,6,-8,0,3,-1}, {1,1,2,3,6,12,23,43,74}, 25] (* _G. C. Greubel_, Sep 11 2016 *)
%t A154324 CoefficientList[Series[(1 - 2 x - x^2 + 5 x^3 - x^4 - 2 x^5 + x^6) / ((1 - x) (1 - x^2))^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 12 2016 *)
%o A154324 (PARI) Vec((1-2*x-x^2+5*x^3-x^4-2*x^5+x^6) / ((1-x)^6*(1+x)^3) + O(x^60)) \\ _Colin Barker_, Sep 12 2016
%K A154324 nonn,easy
%O A154324 0,3
%A A154324 _Paul Barry_, Jan 07 2009