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.

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

Offset

1,8

Links

Table of n, a(n) for n=1..78.

Wikipedia, Polya enumeration theorem.

Example

Triangle begins:
  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,  7,  3, 1, 1;
  0,  89,  82,  40, 18,  7, 3, 1, 1;
  0, 211, 194, 102, 42, 18, 7, 3, 1, 1;
  ...

Crossrefs

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

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

Sequence in context: A135221 A318686 A214546 * A255704 A191347 A106234

Adjacent sequences: A395964 A395965 A395966 * A395968 A395969 A395970

Keyword

nonn,tabl

Author

Seiichi Manyama, May 12 2026

Status

approved