A293019 - OEIS

A293019

Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = - k! * Sum_{i=0..n-1} binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0.

1, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, 0, -2, 2, 1, 1, 0, 0, -6, 9, -2, 1, 0, 0, -6, 0, 4, -9, 1, 0, 0, 0, -24, 100, -95, -9, 1, 0, 0, 0, -24, -60, 570, -414, 50, 1, 0, 0, 0, 0, -120, 240, 798, 49, 267, 1, 0, 0, 0, 0, -120, -360, 4830, -15176, 10088, 413, 1, 0, 0

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OFFSET

0,13

LINKS

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

EXAMPLE

Square array begins:

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

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

0, -1, -2, 0, 0, ...

1, 2, -6, -6, 0, ...

1, 9, 0, -24, -24, ...