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A294589
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j*x^j)^(j^k).
2
1, 1, 1, 1, 1, 3, 1, 1, 5, 6, 1, 1, 9, 14, 14, 1, 1, 17, 36, 42, 25, 1, 1, 33, 98, 140, 103, 56, 1, 1, 65, 276, 498, 481, 289, 97, 1, 1, 129, 794, 1844, 2419, 1774, 690, 198, 1, 1, 257, 2316, 7002, 12745, 12173, 5925, 1771, 354, 1, 1, 513, 6818, 27020, 69283, 89706, 56974, 20076, 4206, 672, 1
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+j/d)) * A(n-j,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
3, 5, 9, 17, 33, ...
6, 14, 36, 98, 276, ...
14, 42, 140, 498, 1844, ...
CROSSREFS
Columns k=0..3 give A006906, A266941, A285241, A294590.
Rows n=0-1 give A000012.
Sequence in context: A271942 A121522 A294582 * A204027 A080842 A368211
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 03 2017
STATUS
approved