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A081095 5th differences of partition numbers A000041. 10

%I

%S -4,5,-7,9,-10,10,-10,12,-16,20,-21,20,-20,24,-30,36,-39,40,-40,45,

%T -54,64,-67,68,-70,81,-94,109,-115,120,-121,135,-152,177,-185,195,

%U -199,227,-249,285,-294,315,-315,357,-385,447,-455,495,-492,565,-590,685,-685,764,-745,866,-883,1047,-1021,1160

%N 5th differences of partition numbers A000041.

%C Comtet appears to say this is nonnegative, which is only true for n sufficiently large.

%C An explanation is given by Odlyzko. - _Moshe Shmuel Newman_, Jun 11 2006

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.

%D A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254

%H Vaclav Kotesovec, <a href="/A081095/b081095.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vincenzo Librandi)

%H Almkvist, Gert, "<a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa61/aa6126.pdf">On the differences of the partition function</a>", Acta Arith., 61.2 (1992), 173-181.

%F a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^5 / (432 * sqrt(2) * n^(7/2)). - _Vaclav Kotesovec_, Oct 06 2017

%t Differences[PartitionsP[Range[0,70]],5] (* _Harvey P. Dale_, Jul 27 2014 *)

%Y Cf. A000041, A002865, A053445, A072380, A081094.

%K sign

%O 0,1

%A _N. J. A. Sloane_, Apr 25 2003

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)