A086364 Triangle read by rows: S_D(n,k) = `Type D' Stirling numbers of the second kind.

1, 2, 2, 2, 9, 4, 2, 27, 36, 10, 2, 65, 195, 140, 26, 2, 143, 840, 1180, 540, 76, 2, 301, 3171, 7735, 6510, 2142, 232, 2, 619, 11060, 43659, 59920, 34692, 8624, 764, 2, 1257, 36707, 223566, 467691, 423612, 180852, 35856, 2620, 2, 2535, 117960, 1071350

Offset: 0

Author

James East, Sep 04 2003

Keywords

• easy
• nonn
• tabl

Crossrefs

Cf. A085483, A086365 (row sums).

Formula

A partition of {-n, ..., -1, 1, ..., n} into nonempty subsets X_1, ..., X_r is called `symmetric' if for each i -X_i = X_j for some j. S_D(n, k) is the number of such symmetric partitions whose induced partition on {1, ..., n} involves k nonempty subsets and none of the X_i are of the form {j, -j}.