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 A262964 #21 Feb 21 2016 20:16:20
%S A262964 1,1,0,1,0,1,1,0,3,0,1,0,6,1,2,1,0,10,4,9,0,1,0,15,10,28,7,5,1,0,21,
%T A262964 20,69,36,30,1
%N A262964 Lower triangular matrix. See comments for definition.
%C A262964 Handmade table created by looking at the "columns" that are separated by zeros in the Mathematica program output. First column is A000012. Second column A000004. Third column A000217. Fourth column A000292. At least a few columns onwards are recognized by the OEIS automated sequence recognition as polynomials.
%C A262964 Row sums are A239605. Alternating row sums are A011782.
%e A262964 Triangle starts and row sums are A239605:
%e A262964 1 = 1
%e A262964 1 0 = 1
%e A262964 1 0 1 = 2
%e A262964 1 0 3 0 = 4
%e A262964 1 0 6 1 2 = 10
%e A262964 1 0 10 4 9 0 = 24
%e A262964 1 0 15 10 28 7 5 = 66
%e A262964 1 0 21 20 69 36 30 1 = 178
%e A262964 Alternating row sums are A011782:
%e A262964 1 = 1
%e A262964 1 -0 = 1
%e A262964 1 -0 1 = 2
%e A262964 1 -0 3 -0 = 4
%e A262964 1 -0 6 -1 2 = 8
%e A262964 1 -0 10 -4 9 -0 = 16
%e A262964 1 -0 15 -10 28 -7 5 = 32
%e A262964 1 -0 21 -20 69 -36 30 -1 = 64
%t A262964 (* To get this number triangle, look at the numbers separated by zeros in the columns *)
%t A262964 (* coefficients (coeff) in power series can be changed *)Clear[t, n, k, i, nn, x];
%t A262964 Clear[x]
%t A262964 coeff = {1, 1000000000000000000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%t A262964 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
%t A262964 mp[m_, e_] :=
%t A262964 If[e == 0, IdentityMatrix@Length@m, MatrixPower[m, e]]; nn =
%t A262964 Length[coeff]; cc = Range[nn]*0 + 1; Monitor[
%t A262964 Do[Clear[t]; t[n_, 1] := t[n, 1] = cc[[n]];
%t A262964 t[n_, k_] :=
%t A262964 t[n, k] =
%t A262964 If[n >= k,
%t A262964 Sum[t[n - i, k - 1], {i, 1, k - 1}] -
%t A262964 Sum[t[n - i, k], {i, 1, k - 1}], 0];
%t A262964 A4 = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
%t A262964 A5 = A4[[1 ;; nn - 1]]; A5 = Prepend[A5, ConstantArray[0, nn]];
%t A262964 cc = Total[
%t A262964 Table[coeff[[n]]*mp[A5, n - 1][[All, 1]], {n, 1, nn}]];, {i, 1,
%t A262964 nn}], i];
%t A262964 cc;
%t A262964 TableForm[A4[[All,1]]]
%Y A262964 Cf. Row sums A239605, alternating row sums A011782, columns: A000012, A000004, A000217, A000292.
%K A262964 tabl,nonn
%O A262964 1,9
%A A262964 _Mats Granvik_, Oct 05 2015