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A081095
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5th differences of partition numbers A000041.
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10
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-4, 5, -7, 9, -10, 10, -10, 12, -16, 20, -21, 20, -20, 24, -30, 36, -39, 40, -40, 45, -54, 64, -67, 68, -70, 81, -94, 109, -115, 120, -121, 135, -152, 177, -185, 195, -199, 227, -249, 285, -294, 315, -315, 357, -385, 447, -455, 495, -492, 565, -590, 685, -685, 764, -745, 866, -883, 1047, -1021, 1160
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OFFSET
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0,1
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COMMENTS
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Comtet appears to say this is nonnegative, which is only true for n sufficiently large.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.
A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^5 / (432 * sqrt(2) * n^(7/2)). - Vaclav Kotesovec, Oct 06 2017
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MATHEMATICA
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Differences[PartitionsP[Range[0, 70]], 5] (* Harvey P. Dale, Jul 27 2014 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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