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A144218 Equals product A*B, where A is an infinite lower triangular matrix with A086246 in every column and B is the diagonal matrix with A001006 as diagonal.

%I A144218 #29 Jan 26 2024 15:13:49
%S A144218 1,1,1,1,1,2,2,1,2,4,4,2,2,4,9,9,4,4,4,9,21,21,9,8,8,9,21,51,51,21,18,
%T A144218 16,18,21,51,127,127,51,42,36,36,42,51,127,323,323,127,102,84,81,84,
%U A144218 102,127,323,835,835,323,254,204,189,189,204,254,323,835,2188
%N A144218 Equals product A*B, where A is an infinite lower triangular matrix with A086246 in every column and B is the diagonal matrix with A001006 as diagonal.
%C A144218 Right border is A001006.
%C A144218 Row sums give A001006 without the initial 1.
%C A144218 Left border is A086246 (A001006 with an additional leading 1).
%C A144218 Sum of n-th row terms = rightmost term of next row.
%H A144218 Paul Barry, <a href="http://arxiv.org/abs/1107.5490">Invariant number triangles, eigentriangles and Somos-4 sequences</a>, arXiv preprint arXiv:1107.5490 [math.CO], 2011.
%e A144218 First few rows of the triangle:
%e A144218     1;
%e A144218     1,   1;
%e A144218     1,   1,   2;
%e A144218     2,   1,   2,   4;
%e A144218     4,   2,   2,   4,   9;
%e A144218     9,   4,   4,   4,   9,  21;
%e A144218    21,   9,   8,   8,   9,  21,  51;
%e A144218    51,  21,  18,  16,  18,  21,  51, 127;
%e A144218   127,  51,  42,  36,  36,  42,  51, 127, 323;
%e A144218   323, 127, 102,  84,  81,  84, 102, 127, 323, 835;
%e A144218   835, 323, 254, 204, 189, 189, 204, 254, 323, 835, 2188;
%e A144218   ...
%e A144218 Row 4 = (4, 2, 2, 4, 9) = termwise products of (4, 2, 1, 1, 1) and (1, 1, 2, 4, 9) = (4*1, 2*1, 1*2, 1*4, 1*9).
%t A144218 nmax = 10;
%t A144218 T[0, 0] = T[1, 0] = 1;
%t A144218 T[n_, 0]  := Hypergeometric2F1[3/2, 1-n, 3, 4] // Abs;
%t A144218 T[n_, n_] := Hypergeometric2F1[(1-n)/2, -n/2, 2, 4];
%t A144218 row[n_] := row[n] = Table[T[m, 0], {m, n, 0, -1}]*Table[T[m, m], {m, 0, n} ];
%t A144218 T[n_, k_] /; 0<k<n := row[n][[k+1]];
%t A144218 Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Aug 07 2018 *)
%Y A144218 Cf. A001006, A086246.
%K A144218 nonn,tabl
%O A144218 0,6
%A A144218 _Gary W. Adamson_, Sep 14 2008
%E A144218 Edited by _Joerg Arndt_, Jan 26 2024