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%I #8 Nov 20 2022 10:52:48
%S 1,1,1,1,3,2,1,6,10,6,1,10,30,42,23,1,15,70,168,207,106,1,21,140,504,
%T 1035,1166,567,1,28,252,1260,3795,6996,7371,3434
%N Eigentriangle, row sums = A125275, shifted.
%C Row sums = A125273 shifted. A125273 = the eigensequence of triangle A085478.
%C Right border = A125273: (1, 1, 2, 6, 23, 106, 567, 3434,...). Sum of n-th row terms = rightmost term in next row.
%F Triangle read by rows, T(n,k) = A085478(n,k) * A125273(k).
%F As infinite lower triangular matrices, A144250 = A085478 * (A125275 * 0^(n-k); where (A125275 * 0^(n-k)) = an infinite lower triangular matrix with A125275: (1, 1, 2, 6, 23, 106, 567, 3434,...) as the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 1, 3, 2;
%e 1, 6, 10, 6;
%e 1, 10, 30, 42, 23;
%e 1, 15, 70, 168, 207, 106;
%e 1, 21, 140, 504, 1035, 1166, 567;
%e ...
%e Row 4 = (1, 10, 30, 42, 23) = termwise products of (1, 10, 15, 7, 1) and (1, 1, 2, 6, 23) = (1*1, 10*1, 15*2, 7*6, 1*23); where (1, 10, 15, 7, 1) = row 4 of triangle A085478. Q
%Y Cf. A125273, A085478.
%K nonn,tabl,more
%O 0,5
%A _Gary W. Adamson_, Sep 16 2008
%E Corrected definition: Eigentriangle, row sums = A125273, shifted. - _Gary W. Adamson_, Nov 05 2008