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 A136398 #10 Jul 05 2019 21:01:46
%S A136398 1,-6,2,15,-13,4,-20,36,-28,8,15,-55,85,-60,16,-6,50,-146,198,-128,32,
%T A136398 1,-27,155,-377,456,-272,64,8,-104,456,-952,1040,-576,128,-1,43,-363,
%U A136398 1289,-2360,2352,-1216,256,-10,190,-1182,3530,-5760,5280,-2560,512
%N A136398 Triangle read by rows of coefficients of Chebyshev-like polynomials P_{n,6}(x) with 0 omitted (exponents in increasing order).
%C A136398 If U_n(x), T_n(x) are Chebyshev's polynomials then U_n(x)=P_{n,0}(x), T_n(x)=P_{n,1}(x).
%C A136398 Let n>=6 and k be of the same parity. Consider a set X consisting of (n+k)/2-6 blocks of the size 2 and an additional block of the size 6, then (-1)^((n-k)/2)a(n,k) is the number of n-6-subsets of X intersecting each block of the size 2.
%H A136398 Michael De Vlieger, <a href="/A136398/b136398.txt">Table of n, a(n) for n = 6..10185</a> (rows 6 <= n <= 200, flattened).
%H A136398 Milan Janjic, <a href="http://www.pmfbl.org/janjic">Two enumerative functions</a>.
%H A136398 M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Janjic/janjic19.html">On a class of polynomials with integer coefficients</a>, JIS 11 (2008) 08.5.2.
%H A136398 Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.
%F A136398 If n>=6 and k are of the same parity then a(n,k)= (-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-6, i)*binomial(n+k-6-2*i, n-6), i=0..(n+k)/2-6) and a(n,k)=0 if n and k are of different parity.
%e A136398 Rows are (1),(-6,2),(15,-13,4),... since P_{6,6}=x^6, P_{7,6}=-6x^5+2x^7, P_{8,6}=15x^4-13x^6+4x^8,...
%p A136398 if modp(n-k, 2)=0 then a[n, k]:=(-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-6, i)*binomial(n+k-6-2*i, n-6), i=0..(n+k)/2-6); end if;
%t A136398 DeleteCases[#, 0] &@ Flatten@ Table[(-1)^((n - k)/2) * Sum[(-1)^i * Binomial[(n + k)/2 - 6, i] Binomial[n + k - 6 - 2 i, n - 6], {i, 0, (n + k)/2 - 6}], {n, 6, 15}, {k, 0 + Boole[OddQ@ n], n, 2}] (* _Michael De Vlieger_, Jul 05 2019 *)
%Y A136398 Cf. A008310, A053117.
%K A136398 sign,tabf
%O A136398 6,2
%A A136398 _Milan Janjic_, Mar 30 2008, revised Apr 05 2008