

A081095


5th differences of partition numbers A000041.


10



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

0,1


COMMENTS

Comtet appears to say this is nonnegative, which is only true for n sufficiently large.
An explanation is given by Odlyzko.  Moshe Shmuel Newman, Jun 11 2006


REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.
A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237254


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
Almkvist, Gert, "On the differences of the partition function", Acta Arith., 61.2 (1992), 173181.


FORMULA

a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^5 / (432 * sqrt(2) * n^(7/2)).  Vaclav Kotesovec, Oct 06 2017


MATHEMATICA

Differences[PartitionsP[Range[0, 70]], 5] (* Harvey P. Dale, Jul 27 2014 *)


CROSSREFS

Cf. A000041, A002865, A053445, A072380, A081094.
Sequence in context: A135186 A011336 A094328 * A080596 A183866 A196004
Adjacent sequences: A081092 A081093 A081094 * A081096 A081097 A081098


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Apr 25 2003


STATUS

approved



