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

0,2

Links

Table of n, a(n) for n=0..48.

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}.

Crossrefs

Cf. A085483, A086365 (row sums).

Sequence in context: A340080 A022459 A060804 * A260662 A228044 A171529

Adjacent sequences: A086361 A086362 A086363 * A086365 A086366 A086367

Keyword

easy,nonn,tabl

Author

James East, Sep 04 2003

Status

approved