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A294609
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*j)) in powers of x.
5
1, 1, 1, 1, 1, 3, 1, 1, 9, 6, 1, 1, 33, 90, 14, 1, 1, 129, 2220, 1154, 25, 1, 1, 513, 59178, 264908, 17427, 56, 1, 1, 2049, 1594836, 67176362, 49163017, 309117, 97, 1, 1, 8193, 43048770, 17181595604, 152662625259, 13120646934, 6285102, 198
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, ...
3, 9, 33, 129, 513, ...
6, 90, 2220, 59178, 1594836, ...
14, 1154, 264908, 67176362, 17181595604, ...
CROSSREFS
Columns k=0..2 give A006906, A294610, A294611.
Rows n=0-1 give A000012.
Cf. A294605.
Sequence in context: A144183 A050153 A294950 * A204180 A319729 A106340
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Nov 04 2017
STATUS
approved