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A342578
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a(n) = n! * [x^n] (Sum_{j>=0} n^(j*(j+1)/2) * x^j/j!)^(1/n) for n > 0, a(0) = 1.
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2
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1, 1, 3, 199, 249337, 6062674201, 3653786369479951, 65709007885111803731947, 40564683796482484146182142025377, 969773549559254966290998252899999751714721, 999999990999996719397362087568018696141879478712251051, 49037072510879011742983689973641327840345400616866967292640434759551
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OFFSET
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0,3
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COMMENTS
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All terms are odd.
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LINKS
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FORMULA
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a(n) == 1 (mod n*(n-1)) for n >= 2 (see "general conjecture" in A178319 and link to proof by Richard Stanley above).
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MAPLE
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a:= n-> `if`(n>0, coeff(series(add(n^binomial(j+1, 2)*
x^j/j!, j=0..n)^(1/n), x, n+1), x, n)*n!, 1):
seq(a(n), n=0..12);
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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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