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Coefficients in a certain Poincaré series [or Poincare series].
3

%I #9 Jan 30 2018 18:57:37

%S 1,1,0,0,1,2,2,2,4,7,9,12,20,32,45,66,105,164,246,372,582,909,1393,

%T 2146,3355,5240,8132,12660,19825,31051,48554,76038,119409,187635,

%U 294760,463520,729980,1150296,1813100,2859948,4515225,7132412

%N Coefficients in a certain Poincaré series [or Poincare series].

%C Let V=Sum_{k=1..infty} V_k be the graded vector space H_*(PC^infty)[1], which has Poincaré series [or Poincare series] p(t)=t/(1-t^2). Let L be the free graded Lie algebra V. There is a graded involution theta on V induced by an involution on PC^infty, which acts on V_{2k+1} as (-1)^k. The sequence gives the dimensions of the +1-eigenspaces of theta on the graded components of L.

%C Lehrer-Segal give a recurrence; both this reference and the Lehrer article give the first 50 terms.

%D G. I. Lehrer and G. B. Segal, Homology stability for classical regular semisimple varieties, Math. Zeit., 236 (2001), 251-290; p. 285.

%H G. I. Lehrer, <a href="/A098787/a098787.pdf">Some sequences arising at the interface of representation theory and homotopy theory</a>

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_, Oct 28 2004