A144107 Eigentriangle, row sums = n!

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

Offset: 1

Author

Gary W. Adamson, Sep 11 2008

Keywords

• nonn
• tabl

Comments

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

Left border = A003319.

Examples

			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]
		

Crossrefs

Cf. A000142, A003319.

Formula

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,...).