This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072380 #12 Oct 06 2017 08:40:05 %S A072380 -1,1,-1,2,-2,3,-2,3,-2,5,-4,7,-3,7,-3,11,-5,15,-4,17,-2,24,-4,32,1, %T A072380 38,5,53,7,70,18,86,33,115,45,152,74,191,109,254,150,331,218,420,307, %U A072380 551,410,716,567,913,767,1186,1015,1529,1358,1951,1799,2513,2344,3222,3079,4096,4009,5237,5173 %N A072380 Third differences of partition numbers A000041. %C A072380 Comtet appears to say this is nonnegative, which is only true for n sufficiently large. %C A072380 An explanation is given by Odlyzko. - _Moshe Shmuel Newman_, Jun 11 2006 %D A072380 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115. %D A072380 A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254 %H A072380 Vaclav Kotesovec, <a href="/A072380/b072380.txt">Table of n, a(n) for n = 0..10000</a> %H A072380 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 A072380 a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (72 * sqrt(2) * n^(5/2)). - _Vaclav Kotesovec_, Oct 06 2017 %t A072380 Differences[PartitionsP[Range[0,70]],3] (* _Harvey P. Dale_, Aug 16 2012 *) %Y A072380 Cf. A000041, A002865, A053445, A081094, A081095. %K A072380 sign %O A072380 0,4 %A A072380 _N. J. A. Sloane_, Apr 25 2003