1,4

Sum of n-th row terms = rightmost term of next row.

Left border = A003319.

Eigentriangle by rows, T(n,k) = A003319(n-k+1)*((n-1)!).

Given an infinite lower triangular matrix with A003319 in every column: (1, 1, 3, 13, 71,...); we apply termwise products of row terms to an equal number of

terms in the factorial sequence: (1, 1, 2, 6, 24,...).

First few rows of the triangle =

1;

1, 1;

3, 1, 2;

13, 3, 2, 6;

71, 13, 6, 6, 24;

461, 71, 26, 18, 24, 120;

3447, 461, 142, 78, 72, 120, 720;

29093, 3447, 922, 426, 312, 360, 720, 5040;

...

Example: Row 4 = (13, 3, 2, 6) = termwise products of (13, 3, 1, 1) and (1, 1, 2, 6) = (13*1, 3*1, 1*2, 1*6); where (13, 3, 1, 1) = the first 4 terms of A003319, reversed. [Line corrected by Brad Fox, Sep 15 2008]

Cf. A000142, A003319.

Sequence in context: A092580 A004468 A145463 this_sequence A163485 A126038 A088363

Adjacent sequences: A144104 A144105 A144106 this_sequence A144108 A144109 A144110

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008