login
A294605
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j*x^j)^(j^(k*j)) in powers of x.
4
1, 1, -1, 1, -1, -2, 1, -1, -8, -1, 1, -1, -32, -73, -1, 1, -1, -128, -2155, -919, 5, 1, -1, -512, -58921, -259477, -13977, 1, 1, -1, -2048, -1593811, -67041751, -48496477, -253640, 13, 1, -1, -8192, -43044673, -17178144301, -152513231553, -13001163543, -5290184, 4
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1+j/d)) * 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, ...
-1, -919, -259477, -67041751, -17178144301, ...
CROSSREFS
Columns k=0..2 give A022661, A294606, A294607.
Rows n=0..1 give A000012, (-1)*A000012.
Sequence in context: A072286 A007375 A294808 * A060865 A078689 A230069
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 04 2017
STATUS
approved