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 A266732 #37 Jul 06 2024 10:30:28
%S A266732 0,10,60,210,560,1260,2520,4620,7920,12870,20020,30030,43680,61880,
%T A266732 85680,116280,155040,203490,263340,336490,425040,531300,657800,807300,
%U A266732 982800,1187550,1425060,1699110,2013760,2373360,2782560,3246320,3769920,4358970,5019420
%N A266732 a(n) = 10*binomial(n+4, 5).
%C A266732 Total number of pips on a set of tetrominoes (4-celled linear dominoes) with up to n pips in each cell.
%H A266732 Colin Barker, <a href="/A266732/b266732.txt">Table of n, a(n) for n = 0..1000</a>
%H A266732 Steve Butler and Pavel Karasik, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Butler/butler7.html">A note on nested sums</a>, J. Int. Seq. (2010) Vol. 13, Issue 4, Art. No. 10.4.4. See p=4 in the last equation on page 3.
%H A266732 Sela Fried, <a href="https://arxiv.org/abs/2406.18923">Counting r X s rectangles in nondecreasing and Smirnov words</a>, arXiv:2406.18923 [math.CO], 2024. See p. 9.
%H A266732 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A266732 From _Colin Barker_, Jan 08 2016: (Start)
%F A266732 a(n) = n*(1+n)*(2+n)*(3+n)*(4+n)/12.
%F A266732 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) for n > 5.
%F A266732 G.f.: 10*x / (1-x)^6.
%F A266732 (End)
%F A266732 a(n) = 10*A000389(n+4). - _R. J. Mathar_, Dec 18 2016
%F A266732 E.g.f.: x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x)/12. - _G. C. Greubel_, Nov 24 2017
%t A266732 Join[{0},10*Binomial[Range[0,40]+5,5]] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{0,10,60,210,560,1260},40] (* _Harvey P. Dale_, Jun 10 2016 *)
%o A266732 (PARI) a(n) = (n*(1+n)*(2+n)*(3+n)*(4+n))/12 \\ _Colin Barker_, Jan 08 2016
%o A266732 (PARI) concat(0, Vec(10*x/(1-x)^6 + O(x^50))) \\ _Colin Barker_, Jan 08 2016
%o A266732 (Magma) [10*Binomial(n+4,5): n in [0..30]]; // _G. C. Greubel_, Nov 24 2017
%Y A266732 Row 4 of array in A129533. Column k=3 in A253283.
%K A266732 nonn,easy
%O A266732 0,2
%A A266732 _Alan Shore_ and _N. J. A. Sloane_, Jan 06 2016