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A292166
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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 - j^k*x^j).
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7
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1, 1, -1, 1, -1, -1, 1, -1, -2, 0, 1, -1, -4, -1, 0, 1, -1, -8, -5, -1, 1, 1, -1, -16, -19, -7, 5, 0, 1, -1, -32, -65, -37, 27, 1, 1, 1, -1, -64, -211, -175, 155, 17, 13, 0, 1, -1, -128, -665, -781, 927, 205, 167, 4, 0, 1, -1, -256, -2059, -3367, 5675, 2129, 2089, 110, 0, 0
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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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A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*j/d)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 02 2017
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-1, -2, -4, -8, -16, ...
0, -1, -5, -19, -65, ...
0, -1, -7, -37, -175, ...
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MATHEMATICA
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A[n_, k_] := A[n, k] = If[n == 0, 1, -(1/n)*Sum[Sum[d^(1+k*j/d), {d, Divisors[j]}]*A[n-j, k], {j, 1, n}]];
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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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