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 A053633 #43 Mar 11 2018 09:53:48
%S A053633 1,1,1,2,1,1,2,2,2,2,4,3,3,3,3,6,5,5,6,5,5,10,9,9,9,9,9,9,16,16,16,16,
%T A053633 16,16,16,16,30,28,28,29,28,28,29,28,28,52,51,51,51,51,52,51,51,51,51,
%U A053633 94,93,93,93,93,93,93,93,93,93,93,172,170,170,172,170,170,172
%N A053633 Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1+x^j) mod x^(n+1)-1.
%C A053633 T(n,k) = number of binary vectors (x_1,...,x_n) satisfying Sum_{i=1..n} i*x_i = k (mod n+1) = size of Varshamov-Tenengolts code VT_k(n).
%D A053633 B. D. Ginsburg, On a number theory function applicable in coding theory, Problemy Kibernetiki, No. 19 (1967), pp. 249-252.
%H A053633 Seiichi Manyama, <a href="/A053633/b053633.txt">Rows n = 0..139, flattened</a>
%H A053633 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Sloane/sloane55.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A053633 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].
%H A053633 N. J. A. Sloane, <a href="http://neilsloane.com/doc/dijen.txt">On single-deletion-correcting codes</a>
%H A053633 <a href="/index/Su#subsetsums">Index entries for sequences related to subset sums modulo m</a>
%H A053633 <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%F A053633 The Maple code gives an explicit formula.
%e A053633 Triangle begins:
%e A053633 k 0 1 2 3 4 5 6 7 8 9
%e A053633 n
%e A053633 0 1;
%e A053633 1 1, 1;
%e A053633 2 2, 1, 1;
%e A053633 3 2, 2, 2, 2;
%e A053633 4 4, 3, 3, 3, 3;
%e A053633 5 6, 5, 5, 6, 5, 5;
%e A053633 6 10, 9, 9, 9, 9, 9, 9;
%e A053633 7 16, 16, 16, 16, 16, 16, 16, 16;
%e A053633 8 30, 28, 28, 29, 28, 28, 29, 28, 28;
%e A053633 9 52, 51, 51, 51, 51, 52, 51, 51, 51, 51;
%e A053633 ...
%e A053633 [Edited by _Seiichi Manyama_, Mar 11 2018]
%p A053633 with(numtheory): A053633 := proc(n,k) local t1,d; t1 := 0; for d from 1 to n do if n mod d = 0 and d mod 2 = 1 then t1 := t1+(1/(2*n))*2^(n/d)*phi(d)*mobius(d/gcd(d,k))/phi(d/gcd(d,k)); fi; od; t1; end;
%t A053633 Flatten[ Table[ CoefficientList[ PolynomialMod[ Product[1+x^j, {j,1,n}], x^(n+1)-1], x], {n,0,11}]] (* _Jean-François Alcover_, May 04 2011 *)
%Y A053633 Cf. A053632, A063776, A300328, A300628. Leading coefficients give A000016, next column gives A000048.
%K A053633 tabl,nonn,easy,nice
%O A053633 0,4
%A A053633 _N. J. A. Sloane_, Mar 22 2000