cp's OEIS Frontend

A124226 Number of partitions of n with even crank minus number of partitions of n with odd crank.

%I A124226 #12 Jul 02 2025 16:02:02
%S A124226 1,-1,2,-1,5,-5,3,-5,6,-10,10,-8,13,-15,15,-16,23,-27,25,-30,35,-40,
%T A124226 42,-45,55,-66,68,-70,86,-95,100,-110,125,-141,150,-161,185,-207,215,
%U A124226 -235,266,-293,310,-335,375,-410,438,-470,521,-575,610,-653,725,-785,835,-900,983,-1070,1140,-1220,1331,-1443,1532
%N A124226 Number of partitions of n with even crank minus number of partitions of n with odd crank.
%C A124226 For a partition p, let l(p) = largest part of p, w(p) = number of 1's in p, m(p) = number of parts of p larger than w(p). The crank of p is given by l(p) if w(p) = 0, otherwise m(p)-w(p).
%F A124226 G.f.: 2*x + Product_{i>=1} (1-x^i)/(1+x^i)^2.
%F A124226 a(n) = A132970(n) unless n=1. - _Michael Somos_, Jul 27 2015
%F A124226 a(n) ~ (-1)^n * exp(Pi*sqrt(n/6)) / (2*sqrt(n)). - _Vaclav Kotesovec_, Oct 14 2017
%e A124226 G.f. = 1 - x + 2*x^2 - x^3 + 5*x^4 - 5*x^5 + 3*x^6 - 5*x^7 + 6*x^8 + ...
%p A124226 p:=2*q + product((1-q^i)/(1+q^i)^2, i=1..200): s:=series(p, q, 200): for j from 0 to 199 do printf(`%d,`,coeff(s,q, j)) od: # _James Sellers_, Nov 30 2006
%Y A124226 Cf. A124227, A124228, A132970.
%K A124226 easy,sign
%O A124226 0,3
%A A124226 _Vladeta Jovovic_, Oct 20 2006
%E A124226 More terms from _James Sellers_, Nov 30 2006