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A294950
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^(k*j)*x^j)^j in powers of x.
3
1, 1, 1, 1, 1, 3, 1, 1, 9, 6, 1, 1, 33, 90, 13, 1, 1, 129, 2220, 1162, 24, 1, 1, 513, 59178, 265132, 17435, 48, 1, 1, 2049, 1594836, 67180330, 49163241, 310193, 86, 1, 1, 8193, 43048770, 17181660628, 152662629227, 13121450895, 6286826, 160
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, ...
3, 9, 33, 129, 513, ...
6, 90, 2220, 59178, 1594836, ...
13, 1162, 265132, 67180330, 17181660628, ...
24, 17435, 49163241, 152662629227, 476855156157129, ...
CROSSREFS
Columns k=0..2 give A000219, A294813, A294954.
Rows n=0+1, 2 give A000012, A087289.
Sequence in context: A171435 A144183 A050153 * A294609 A204180 A319729
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 12 2017
STATUS
approved