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A284992
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1+x^j)^(j^k) in powers of x.
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8
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1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 5, 2, 1, 1, 8, 13, 8, 3, 1, 1, 16, 35, 31, 16, 4, 1, 1, 32, 97, 119, 83, 28, 5, 1, 1, 64, 275, 457, 433, 201, 49, 6, 1, 1, 128, 793, 1763, 2297, 1476, 487, 83, 8, 1, 1, 256, 2315, 6841, 12421, 11113, 4962, 1141, 142, 10, 1, 1
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f. of column k: Product_{j>=1} (1+x^j)^(j^k).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, 64, 128, ...
2, 5, 13, 35, 97, 275, 793, 2315, ...
2, 8, 31, 119, 457, 1763, 6841, 26699, ...
3, 16, 83, 433, 2297, 12421, 68393, 382573, ...
4, 28, 201, 1476, 11113, 85808, 678101, 5466916, ...
5, 49, 487, 4962, 52049, 561074, 6189117, 69540142, ...
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*binomial(i^k, j), j=0..n/i)))
end:
A:= (n, k)-> b(n$2, k):
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
Sum[b[n - i*j, i - 1, k]*Binomial[i^k, j], {j, 0, n/i}]]];
A[n_, k_] := b[n, n, k];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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