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Erroneous duplicate of A125026.
1

%I #22 Feb 20 2022 14:48:22

%S 1,3,2,5,7,3,7,15,13,4,9,26,34,21,5,11,40,70,65,31,6,13,57,125,155,

%T 111,43,7,15,77,203,315,301,175,57,8,17,100,308,574,686,532,260,73,9,

%U 19,126,444,966,1386,1344,876369,91,10

%N Erroneous duplicate of A125026.

%C This sequence was initially defined as "A051340 * A007318". However, the matrix product A051340 * A007318 is not well defined, because all elements of A051340 are strictly positive integers, as are all elements of the lower left of A007318. Therefore the matrix A051340 must be truncated to its lower left (setting A[i,j]=0 if j>i), which actually equals A130296. Then the product yields this sequence, which is identical to A125026.

%C Row sums = A099035 (not A083706 as stated initially): (1, 5, 15, 39, 95, 223, 511, ...).

%F (A051340) * A007318 as infinite lower triangular matrices. [Here (A051340) is that matrix with the upper right triangle set to zero, which is actually A130296. - _M. F. Hasler_, Aug 15 2015]

%e First few rows of the triangle A125026:

%e 1;

%e 3, 2;

%e 5, 7, 3;

%e 7, 15, 13, 4;

%e 9, 26, 34, 21, 5;

%e 11, 40, 70, 65, 31, 6;

%e 13, 57, 125, 155, 111, 43, 7;

%e ...

%Y Cf. A051340, A099035.

%K dead

%O 1,2

%A _Gary W. Adamson_, May 20 2007

%E Restored and edited by _M. F. Hasler_, Aug 15 2015