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 A157905 #11 Feb 08 2022 23:16:26
%S A157905 1,1,1,1,1,2,1,1,2,4,2,1,2,4,8,3,2,2,4,8,17,6,3,4,4,8,17,36,11,6,6,8,
%T A157905 8,17,36,78,23,11,12,12,16,17,36,78,170,47,23,22,24,24,34,36,78,170,
%U A157905 375,106,47,46,44,48,51,72,78,170,375,833
%N A157905 Triangle read by rows, T(n,k) = A000055(n-k) * (A157904 * 0^(n-k)).
%C A157905 As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.
%F A157905 Triangle read by rows, T(n,k) = A000055(n-k) * (A157904 * 0^(n-k)). A000055(n-k) = an infinite lower triangular matrix with A000055 in every column: (1, 1, 1, 1, 2, 3, 6, 11, 23, ...). (A157904 * 0^(n-k)) = a matrix with A157904 as the diagonal and the rest zeros.
%e A157905 First few rows of the triangle =
%e A157905 1;
%e A157905 1, 1;
%e A157905 1, 1, 2;
%e A157905 1, 1, 2, 4;
%e A157905 2, 1, 2, 4, 8;
%e A157905 3, 2, 2, 4, 8, 17;
%e A157905 6, 3, 4, 4, 8, 17, 36;
%e A157905 11, 6, 6, 8, 8, 17, 36, 78;
%e A157905 23, 11, 12, 12, 16, 17, 36, 78, 170;
%e A157905 47, 23, 22, 24, 24, 34, 36, 78, 170, 375;
%e A157905 106, 47, 46, 44, 48, 51, 72, 78, 170, 375, 833;
%e A157905 235, 106, 94, 92, 88, 102, 108, 156, 170, 375, 833, 1870;
%e A157905 ...
%e A157905 Row 5 = (3, 2, 2, 4, 8, 17) = termwise products of (3, 2, 1, 1, 1, 1) and (1, 1, 2, 4, 8, 17).
%t A157905 b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d b[d], {d, Divisors[j]}] b[n - j], {j, 1, n - 1}]/(n - 1)];
%t A157905 t[n_] := t[n] = If[n == 0, 1, b[n] - (Sum[b[k] b[n - k], {k, 1, n - 1}] - If[OddQ[n], 0, b[n/2]])/2];
%t A157905 u[n_] := u[n] = If[n <= 0, 1, Sum[t[i] u[n - i - 1], {i, 0, n}]];
%t A157905 c[0] = 0; c[1] = 1; c[n_] := c[n] = Sum[d c[d] c[n - j], {j, 1, n - 1}, {d, Divisors[j]}]/(n - 1);
%t A157905 v[0] = 1; v[n_] := c[n] - (Sum[c[k] c[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, c[n/2], 0])/2;
%t A157905 T[n_, k_] := v[n - k] u[k - 1];
%t A157905 Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Sep 21 2020, after _Alois P. Heinz_ in A000055 and A157904 *)
%Y A157905 Cf. A000055 (first column), A157904 (row sums).
%K A157905 nonn,tabl
%O A157905 0,6
%A A157905 _Gary W. Adamson_, Mar 08 2009