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Triangle, antidiagonals of an array generated from A130460.
3

%I #11 Feb 21 2022 00:15:04

%S 1,1,1,1,1,1,1,1,2,1,1,1,2,3,1,1,1,2,6,4,1,1,1,2,6,12,5,1,1,1,2,6,24,

%T 20,6,1,1,1,2,6,24,60,30,7,1,1,1,2,6,24,120,120,42,8,1,1,1,2,6,24,120,

%U 360,210,56,9,1,1,1,2,6,24,120,720,840,336,72,10,1,1,1,2,6,24,120,720,2520

%N Triangle, antidiagonals of an array generated from A130460.

%C Rows tend to the factorials: (1, 1, 2, 6, 24, ...). Row sums = A130476: (1, 2, 3, 5, 8, 15, 28, 61, 132, ...).

%F Let A130460 = M, an infinite lower triangular matrix and V = [1, 1, 1, ...], the first row of an array. Perform M * V = second row, ...; (n+1)-th row = M * n-th row. The triangle = antidiagonals of the array.

%e The array =

%e 1, 1, 1, 1, 1, 1, ...

%e 1, 1, 2, 3, 4, 5, ...

%e 1, 1, 2, 6, 12, 20, ...

%e 1, 1, 2, 6, 24, 60, ...

%e 1, 1, 2, 6, 24, 120, ...

%e 1, 1, 2, 6, 24, 120, ...

%e ...

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 2, 1;

%e 1, 1, 2, 3, 1;

%e 1, 1, 2, 6, 4, 1;

%e 1, 1, 2, 6, 12, 5, 1;

%e 1, 1, 2, 6, 24, 20, 6, 1;

%e 1, 1, 2, 6, 24, 60, 30, 7, 1;

%e ...

%Y Cf. A130460, A130476, A130477, A130478.

%K nonn,tabl

%O 0,9

%A _Gary W. Adamson_, May 28 2007

%E a(23) and a(38) corrected by _Gionata Neri_, Jun 22 2016