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A293134
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-x^(k+1)/(1+x)).
5
1, 1, -1, 1, 0, 3, 1, 0, -2, -13, 1, 0, 0, 6, 73, 1, 0, 0, -6, -12, -501, 1, 0, 0, 0, 24, 0, 4051, 1, 0, 0, 0, -24, -120, 240, -37633, 1, 0, 0, 0, 0, 120, 1080, -2520, 394353, 1, 0, 0, 0, 0, -120, -720, -10080, 21840, -4596553, 1, 0, 0, 0, 0, 0, 720, 5040, 100800
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1, A(1,k) = A(2,k) = ... = A(k,k) = 0 and A(n,k) = (-1)^(k+1) * Sum_{i=k..n-1} (-1)^i*(i+1)!*binomial(n-1,i)*A(n-1-i,k) for n > k.
EXAMPLE
Square array begins:
1, 1, 1, 1, ...
-1, 0, 0, 0, ...
3, -2, 0, 0, ...
-13, 6, -6, 0, ...
73, -12, 24, -24, ...
-501, 0, -120, 120, ...
CROSSREFS
Columns k=0..2 give A293125, A293122, A293123.
Rows n=0..1 give A000012, (-1)*A000007.
Main diagonal gives A000007.
A(n,n-1) gives (-1)*A000142(n).
Sequence in context: A357438 A324173 A355666 * A293053 A355652 A355665
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Sep 30 2017
STATUS
approved