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A294254 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1-x^j) - 1). 8
1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, -1, 0, 1, -1, -1, 11, 1, 0, 1, -1, -1, 5, -23, -1, 0, 1, -1, -1, 5, 25, -101, 1, 0, 1, -1, -1, 5, 1, -41, 991, -1, 0, 1, -1, -1, 5, 1, 199, -1769, -1849, 1, 0, 1, -1, -1, 5, 1, 79, -1409, 7181, -24751, -1, 0, 1, -1, -1, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,19
LINKS
FORMULA
B(j,k) is the coefficient of Product_{i=1..k} (1-x^i).
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
0, -1, -1, -1, -1, ...
0, 1, -1, -1, -1, ...
0, -1, 11, 5, 5, ...
0, 1, -23, 25, 1, ...
0, -1, -101, -41, 199, ...
CROSSREFS
Columns k=0..5 give A000007, A033999, A294255, A294256, A294257, A294258.
Rows n=0 gives A000012.
Main diagonal gives A294260.
Cf. A294250.
Sequence in context: A157712 A266379 A158215 * A216792 A359215 A260237
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Oct 26 2017
STATUS
approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)