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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.
4
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
OFFSET
0,13
LINKS
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, ...
CROSSREFS
Columns k=0-4 give: A000587, A292952, A293016, A293017, A293018.
Rows n=0 gives A000012.
Sequence in context: A349802 A368753 A345907 * A376590 A087479 A263343
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Sep 28 2017
STATUS
approved