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A293051
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{i=0..k} x^i/i! - exp(x)).
6
1, 1, -1, 1, 0, 0, 1, 0, -1, 1, 1, 0, 0, -1, 1, 1, 0, 0, -1, 2, -2, 1, 0, 0, 0, -1, 9, -9, 1, 0, 0, 0, -1, -1, 9, -9, 1, 0, 0, 0, 0, -1, 9, -50, 50, 1, 0, 0, 0, 0, -1, -1, 34, -267, 267, 1, 0, 0, 0, 0, 0, -1, -1, 90, -413, 413, 1, 0, 0, 0, 0, 0, -1, -1, 34, -71
OFFSET
0,20
LINKS
FORMULA
E.g.f. of column k: Product_{i>k} exp(-x^i/i!).
A(0,k) = 1, A(1,k) = A(2,k) = ... = A(k,k) = 0 and A(n,k) = - Sum_{i=k..n-1} binomial(n-1,i)*A(n-1-i,k) for n > k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, 0, 0, 0, 0, ...
0, -1, 0, 0, 0, ...
1, -1, -1, 0, 0, ...
1, 2, -1, -1, 0, ...
-2, 9, -1, -1, -1, ...
CROSSREFS
Columns k=0..4 give A000587, A293037, A293038, A293039, A293040.
Rows n=0..1 give A000012, (-1)*A000007.
Main diagonal gives A000007.
Sequence in context: A016270 A219493 A284092 * A049783 A287320 A210502
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Sep 29 2017
STATUS
approved