A170982 - OEIS

%I #17 Jan 04 2021 04:07:49

%S 1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,2,2,0,1,3,1,0,1,4,1,0,3,4,1,0,4,

%T 5,1,1,6,5,0,2,7,5,0,3,10,4,0,5,10,4,0,8,12,3,2,10,12,2,2,13,12,1,4,

%U 16,10,1,6,18,10,0,10,19,7,1,12,20,6,2,16,19,4,3,18,18,3,5,22,16,1,8,22,13,1

%N Expansion of (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-1)) for m = 10.

%C (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-1)) is the Poincaré polynomial for O(2m).

%D H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.

%H Nathaniel Johnston, <a href="/A170982/b170982.txt">Table of n, a(n) for n = 0..190</a>

%o (PARI) my(m=10, x='x+O('x^189)); Vec((1+x^(2*m-1))*prod(i=1, m-1, 1+x^(4*i-1))) \\ _Jinyuan Wang_, Mar 08 2020

%K nonn,fini,full,easy

%O 0,19

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