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A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

%I A159974 #6 Feb 09 2022 08:34:05
%S A159974 1,1,1,2,1,2,3,2,2,5,4,3,4,5,12,5,4,6,10,12,28,6,5,8,15,24,28,65,7,6,
%T A159974 10,20,36,56,65,151,8,7,12,25,48,84,130,151,351,9,8,14,30,60,112,195,
%U A159974 302,351,816,10,9,16,35,72,140,260,453,702,816,1897
%N A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.
%C A159974 Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...).
%C A159974 As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.
%C A159974 A034943 starting (1, 2, 5, 12, 28, ...) = the INVERT transform of (1, 1, 2, 3, 4, 5, ...).
%F A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.
%e A159974 First few rows of the triangle:
%e A159974    1;
%e A159974    1, 1;
%e A159974    2, 1,  2;
%e A159974    3, 2,  2,  5;
%e A159974    4, 3,  4,  5, 12;
%e A159974    5, 4,  6, 10, 12,  28;
%e A159974    6, 5,  8, 15, 24,  28,  65;
%e A159974    7, 6, 10, 20, 36,  56,  65, 151;
%e A159974    8, 7, 12, 25, 48,  84, 130, 151, 351;
%e A159974    9, 8, 14, 30, 60, 112, 195, 302, 351, 816;
%e A159974   10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897;
%e A159974   ...
%e A159974 Example: row 6 = (4, 3, 4, 5, 12) = termwise products of (1, 1, 2, 5, 12) and (4, 3, 2, 1, 1).
%Y A159974 Cf. A034943.
%K A159974 nonn,tabl
%O A159974 2,4
%A A159974 _Gary W. Adamson_, Apr 28 2009