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 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 (list; graph; refs; listen; history; text; internal format)
 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. 237-254 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), 173-181. 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

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Last modified December 18 14:26 EST 2018. Contains 318229 sequences. (Running on oeis4.)