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A294808
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j^(k*j)*x^j)^j in powers of x.
4
1, 1, -1, 1, -1, -2, 1, -1, -8, -1, 1, -1, -32, -73, 0, 1, -1, -128, -2155, -927, 4, 1, -1, -512, -58921, -259701, -13969, 4, 1, -1, -2048, -1593811, -67045719, -48496253, -254580, 7, 1, -1, -8192, -43044673, -17178209325, -152513227585, -13001952944, -5288596, 3
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j)) * A(n-j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-2, -8, -32, -128, -512, ...
-1, -73, -2155, -58921, -1593811, ...
0, -927, -259701, -67045719, -17178209325, ...
4, -13969, -48496253, -152513227585, -476819162106101, ...
CROSSREFS
Columns k=0..2 give A073592, A294809, A294953.
Rows n=0..2 give A000012, (-1)*A000012, (-1)*A004171.
Sequence in context: A354986 A072286 A007375 * A294605 A060865 A078689
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 09 2017
STATUS
approved