

A130461


Triangle, antidiagonals of an array generated from A130460.


3



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, 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, 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
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OFFSET

0,9


COMMENTS

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


LINKS

Table of n, a(n) for n=0..85.


FORMULA

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 * nth row. The triangle = antidiagonals of the array.


EXAMPLE

The array =
1,...1,...1,...1,....1,....1,...
1,...1,...2,...3,....4,....5,...
1,...1,...2,...6,...12,...20,...
1,...1,...2,...6,...24,...60,...
1,...1,...2,...6,...24,..120,...
1,...1,...2,...6,...24,..120,...
...
First few rows of the triangle are:
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, 20, 6, 1;
1, 1, 2, 6, 24, 60, 30, 7, 1;
...


CROSSREFS

Cf. A130460, A130476, A130477, A130478.
Sequence in context: A238888 A179748 A096670 * A225631 A306209 A267482
Adjacent sequences: A130458 A130459 A130460 * A130462 A130463 A130464


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, May 28 2007


EXTENSIONS

a(23) and a(38) corrected by Gionata Neri, Jun 22 2016


STATUS

approved



