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 A188646 #49 Jan 03 2019 03:11:45
%S A188646 1,1,1,1,13,1,1,181,33,1,1,2521,1121,61,1,1,35113,38081,3781,97,1,1,
%T A188646 489061,1293633,234361,9505,141,1,1,6811741,43945441,14526601,931393,
%U A188646 20021,193,1,1,94875313,1492851361,900414901,91267009,2842841,37441,253,1
%N A188646 Array of a(n)=a(n-1)*k-((k-1)/(k^n)) where a(0)=1 and k=(sqrt(x^2-1)+x)^2 for integers x>=1.
%C A188646 Conjecture: Given function f(x, y)=(sqrt(x^2+y)+x)^2; constant k=f(x, y); and initial term a(0)=1; then for all integers x>=1 and y=[+-]1, k may be irrational, but sequence a(n)=a(n-1)*k-((k-1)/(k^n)) always produces integer sequences; y=-1 results shown here; y=1 results are A188647.
%C A188646 Also square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is (1/n) * T_{2*k+1}(n), with the Chebyshev polynomials of the first kind (type T). - _Seiichi Manyama_, Jan 01 2019
%H A188646 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%H A188646 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A188646 A(n,k) = 2 * A188644(n,k) - A(n,k-1).
%F A188646 A(n,k) = Sum_{j=0..k} binomial(2*k+1,2*j+1)*(n^2-1)^(k-j)*n^(2*j). - _Seiichi Manyama_, Jan 01 2019
%e A188646 Square array begins:
%e A188646 | 0 1 2 3 4
%e A188646 -----+---------------------------------------------
%e A188646 1 | 1, 1, 1, 1, 1, ...
%e A188646 2 | 1, 13, 181, 2521, 35113, ...
%e A188646 3 | 1, 33, 1121, 38081, 1293633, ...
%e A188646 4 | 1, 61, 3781, 234361, 14526601, ...
%e A188646 5 | 1, 97, 9505, 931393, 91267009, ...
%e A188646 6 | 1, 141, 20021, 2842841, 403663401, ...
%e A188646 7 | 1, 193, 37441, 7263361, 1409054593, ...
%e A188646 8 | 1, 253, 64261, 16322041, 4145734153, ...
%e A188646 9 | 1, 321, 103361, 33281921, 10716675201, ...
%e A188646 10 | 1, 397, 158005, 62885593, 25028308009, ...
%e A188646 11 | 1, 481, 231841, 111746881, 53861764801, ...
%e A188646 12 | 1, 573, 328901, 188788601, 108364328073, ...
%e A188646 13 | 1, 673, 453601, 305726401, 206059140673, ...
%e A188646 14 | 1, 781, 610741, 477598681, 373481557801, ...
%e A188646 15 | 1, 897, 805505, 723342593, 649560843009, ...
%e A188646 ...
%t A188646 A[n_, k_] := 1/n ChebyshevT[2k+1, n];
%t A188646 Table[A[n-k, k], {n, 1, 9}, {k, n-1, 0, -1}] // Flatten (* _Jean-François Alcover_, Jan 02 2019, after _Seiichi Manyama_ *)
%Y A188646 Row 1-8 give A000012, A001570, A077420, A302329, A302330, A302331, A302332, A253880.
%Y A188646 Column 1 is A082109(n-1).
%Y A188646 Cf. A188644, A188647 (f(x, y) as above with y=1).
%Y A188646 Diagonal gives A322904.
%K A188646 nonn,tabl
%O A188646 0,5
%A A188646 _Charles L. Hohn_, Apr 06 2011
%E A188646 Edited and extended by _Seiichi Manyama_, Jan 01 2019