A169987 - OEIS

%I #16 Sep 15 2024 11:04:54

%S 1,1,0,1,1,1,1,1,2,1,1,1,1,1,0,1,1

%N Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=4.

%C Product_{i=0..m-1} (1 + x^(2*i+1)) is the Poincaré polynomial for GL(m).

%C Number of self-conjugate partitions of n into at most 4 parts. Also, number of partitions of n into distinct odd parts not larger than 7. - _Álvar Ibeas_, Jul 30 2020

%D H. Weyl, The Classical Groups, Princeton, 1946, see p. 233.

%p f:=proc(m) local x,t1; t1:=mul((1+x^(2*i+1)),i=0..m-1); series(expand(t1),x,200); end;

%p g:=m->seriestolist(f(m)); g(4);

%t CoefficientList[Series[Product[1+x^(2i+1),{i,0,3}],{x,0,20}],x] (* _Harvey P. Dale_, Sep 15 2024 *)

%Y Cf. A169987-A169995 (these are all rows of the triangle in A178666), A000700.

%K nonn,fini,full

%O 0,9

%A _N. J. A. Sloane_, Aug 29 2010