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 A276159 #48 Feb 16 2025 08:33:36
%S A276159 1,16,106,416,1211,2912,6132,11712,20757,34672,55198,84448,124943,
%T A276159 179648,252008,345984,466089,617424,805714,1037344,1319395,1659680,
%U A276159 2066780,2550080,3119805,3787056,4563846,5463136,6498871,7686016,9040592,10579712,12321617,14285712,16492602,18964128
%N A276159 Convolution of nonzero octagonal numbers (A000567) with themselves.
%H A276159 OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A276159 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H A276159 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1)
%F A276159 O.g.f.: (1 + 5*x)^2/(1 - x)^6.
%F A276159 E.g.f.: (30 + 450*x + 1125*x^2 + 725*x^3 + 150*x^4 + 9*x^5)*exp(x)/30.
%F A276159 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A276159 a(n) = (n + 1)*(n + 2)*(n + 3)*(9*n^2 + 6*n + 5)/30.
%t A276159 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 16, 106, 416, 1211, 2912}, 36]
%t A276159 Table[(n + 1) (n + 2) (n + 3) ((9 n^2 + 6 n + 5)/30), {n, 0, 35}]
%Y A276159 Cf. A000567.
%Y A276159 Cf. similar sequences of the convolution of k-gonal numbers with themselves listed in A271662.
%K A276159 nonn,easy
%O A276159 0,2
%A A276159 _Ilya Gutkovskiy_, Sep 05 2016