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A368721
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a(n) = Product_{j=1..n, k=1..n} (j^4 + k^4 + n^4).
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3
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OFFSET
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0,2
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COMMENTS
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In general, for m>0, limit_{n->oo} (Product_{j=1..n, k=1..n} (j^m + k^m + n^m))^(1/(n^2)) / n^m = exp(Integral_{x=0..1, y=0..1} log(x^m + y^m + 1) dy dx) = 3 / exp(HurwitzLerchPhi(-1/2, 1, 1 + 1/m)/2 + Integral_{x=0..1} HurwitzLerchPhi(-1/(1 + x^m), 1, 1 + 1/m) / (1 + x^m) dx).
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LINKS
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FORMULA
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Limit_{n->oo} a(n)^(1/(n^2)) / n^4 = exp(Integral_{x=0..1, y=0..1} log(x^4 + y^4 + 1) dy dx) = 1.35451345305131009729671041498902524074679186355643287514556358...
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MATHEMATICA
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Table[Product[j^4 + k^4 + n^4, {j, 1, n}, {k, 1, n}], {n, 0, 6}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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