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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

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

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.

Cf. A293669, A334568.

Sequence in context: A322356 A337337 A119788 * A059592 A295554 A319099

Adjacent sequences:  A334558 A334559 A334560 * A334562 A334563 A334564

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, May 06 2020

STATUS

approved

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Last modified August 1 22:01 EDT 2021. Contains 346408 sequences. (Running on oeis4.)