A395967 - OEIS

A395967

Triangle T(n,k), n >= 1, 0 <= k <= n-1, read by rows, where T(n,k) = [x^n] x * cycle_index(S_k, B(x)-1), where B(x) is g.f. for A000598.

%I #17 May 12 2026 08:50:55

%S 1,0,1,0,1,1,0,2,1,1,0,4,3,1,1,0,8,6,3,1,1,0,17,15,7,3,1,1,0,39,33,17,

%T 7,3,1,1,0,89,82,40,18,7,3,1,1,0,211,194,102,42,18,7,3,1,1,0,507,482,

%U 249,109,43,18,7,3,1,1,0,1238,1188,631,269,111,43,18,7,3,1,1

%N Triangle T(n,k), n >= 1, 0 <= k <= n-1, read by rows, where T(n,k) = [x^n] x * cycle_index(S_k, B(x)-1), where B(x) is g.f. for A000598.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem">Polya enumeration theorem</a>.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 2, 1, 1;

%e 0, 4, 3, 1, 1;

%e 0, 8, 6, 3, 1, 1;

%e 0, 17, 15, 7, 3, 1, 1;

%e 0, 39, 33, 17, 7, 3, 1, 1;

%e 0, 89, 82, 40, 18, 7, 3, 1, 1;

%e 0, 211, 194, 102, 42, 18, 7, 3, 1, 1;

%e ...

%Y Columns k=0..5 give A063524, A000598(n-1), A000599, A000600, A000633(n-1) (A036669), A036670.

%Y T(2*k+1,k) gives A395968.

%K nonn,tabl

%O 1,8

%A _Seiichi Manyama_, May 12 2026