A124226 - OEIS

%I #11 May 11 2019 18:36:29

%S 1,-1,2,-1,5,-5,3,-5,6,-10,10,-8,13,-15,15,-16,23,-27,25,-30,35,-40,

%T 42,-45,55,-66,68,-70,86,-95,100,-110,125,-141,150,-161,185,-207,215,

%U -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 Number of partitions of n with even crank minus number of partitions of n with odd crank.

%C 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 G.f.: 2*x + Product_{i>=1} (1-x^i)/(1+x^i)^2.

%F a(n) = A132970(n) unless n=1. - _Michael Somos_, Jul 27 2015

%F a(n) ~ (-1)^n * exp(Pi*sqrt(n/6)) / (2*sqrt(n)). - _Vaclav Kotesovec_, Oct 14 2017

%e 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 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 A. Sellers_, Nov 30 2006

%Y Cf. A124227, A124228, A132970.

%K easy,sign

%O 0,3

%A _Vladeta Jovovic_, Oct 20 2006

%E More terms from _James A. Sellers_, Nov 30 2006