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A169987 Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=4. 14

%I #14 Jan 07 2021 01:19:13

%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);

%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

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Last modified April 19 05:02 EDT 2024. Contains 371782 sequences. (Running on oeis4.)