login
A294951
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(-Sum_{j>=1} sigma_k(j) * x^j).
1
1, 1, -1, 1, -1, -3, 1, -1, -5, -1, 1, -1, -9, -7, 1, 1, -1, -17, -31, 1, 279, 1, -1, -33, -115, -23, 839, 301, 1, -1, -65, -391, -215, 3399, 4171, 12263, 1, -1, -129, -1267, -1319, 17519, 41311, 54305, 5601, 1, -1, -257, -3991, -6839, 102999, 387031, 473129, 102817, -431281
OFFSET
0,6
FORMULA
A(0,k) = 1 and A(n,k) = -(n-1)! * Sum_{j=1..n} j*sigma_k(j)*A(n-j,k)/(n-j)! for n > 0.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-3, -5, -9, -17, -33, ...
-1, -7, -31, -115, -391, ...
1, 1, -23, -215, -1319, ...
279, 839, 3399, 17519, 102999, ...
CROSSREFS
Columns k=0..2 give A294402, A294403, A294404.
Rows n=0..2 give A000012, (-1)*A000012, (-1)*A000051(n+1).
Cf. A294947.
Sequence in context: A098084 A016562 A087501 * A101443 A228037 A184726
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 12 2017
STATUS
approved