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A334561 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals downwards, where column k is the expansion of e.g.f. exp(-Sum_{j=1..k} x^j). 5
1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 5, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 25, -41, 1, 1, -1, -1, -1, 1, 19, 31, -1, 1, -1, -1, -1, 1, 139, -209, 461, 1, 1, -1, -1, -1, 1, 19, 151, -2269, -895, -1, 1, -1, -1, -1, 1, 19, 871, -1429, 2801, -6481, 1, 1, -1, -1, -1, 1, 19, 151, 1091, -19039, 68615, 22591, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,14
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = - (n-1)! * Sum_{j=1..min(k,n)} j*A(n-j,k)/(n-j)!.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, -1, -1, ...
1, -1, -1, -1, -1, -1, -1, ...
-1, 5, -1, -1, -1, -1, -1, ...
1, 1, 25, 1, 1, 1, 1, ...
-1, -41, 19, 139, 19, 19, 19, ...
1, 31, -209, 151, 871, 151, 151, ...
CROSSREFS
Columns k=1..5 give A033999, A000321, A334562, A334564, A334565.
Main diagonal gives A293116.
Sequence in context: A322356 A337337 A119788 * A059592 A295554 A319099
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, May 06 2020
STATUS
approved

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Last modified March 18 22:33 EDT 2024. Contains 370951 sequences. (Running on oeis4.)