A293287 -id:A293287

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A290217

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(1 + Sum_{j=1..k} j*x^(j*i)).

+10
6

1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, -2, -1, 0, 1, -1, -2, 3, 1, 0, 1, -1, -2, 0, -1, -1, 0, 1, -1, -2, 0, 5, -5, 1, 0, 1, -1, -2, 0, 1, 1, 9, -1, 0, 1, -1, -2, 0, 1, 9, -12, 3, 2, 0, 1, -1, -2, 0, 1, 4, -4, -3, -20, -2, 0, 1, -1, -2, 0, 1, 4, 6, -15, 31, 16, 2

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,13

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, ...

0, -1, -1, -1, -1, ...

0, 0, -2, -2, -2, ...

0, -1, 3, 0, 0, ...

0, 1, -1, 5, 1, ...

0, -1, -5, 1, 9, ...

CROSSREFS

Columns k=0..3 give A000007, A081362, A293287, A290395.

Rows n=0..1 give A000012, (-1)*A057427.

Main diagonal gives A258210.

Cf. A290216, A293307.

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, Oct 06 2017

STATUS

approved

A293285

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} j!*x^(j*i)).

+10
3

1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, -2, -1, 0, 1, -1, -2, 3, 1, 0, 1, -1, -2, -3, -1, -1, 0, 1, -1, -2, -3, 11, -5, 1, 0, 1, -1, -2, -3, -13, 7, 9, -1, 0, 1, -1, -2, -3, -13, 55, -15, 3, 2, 0, 1, -1, -2, -3, -13, -65, 33, -63, -20, -2, 0, 1, -1, -2, -3, -13, -65