A058936 Decomposition of Stirling's S(n,2) based on associated numeric partitions.

0, 1, 3, 8, 3, 30, 20, 144, 90, 40, 840, 504, 420, 5760, 3360, 2688, 1260, 45360, 25920, 20160, 18144, 403200, 226800, 172800, 151200, 72576, 3991680, 2217600, 1663200, 1425600, 1330560, 43545600, 23950080, 17740800, 14968800, 13685760, 6652800, 518918400

Offset: 1

Author

Alford Arnold, Jan 11 2001

Keywords

• nonn
• tabf

Comments

These values also appear in a wider context when counting elements of finite groups by cycle structure. For example, the alternating group on four symbols has 12 elements; eight associated with the partition 3+1, three associated with 2+2 and the identity associated with 1+1+1+1. The cross-referenced sequences are all associated with similar numeric partitions and "M2" weights.

Examples

			Triangle begins:
  0;
  1;
  3;
  8, 3;
  30, 20;
  144, 90, 40;
  840, 504, 420;
  ...
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831.

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A000012, A000035, A000027, A004526, A022003, A008619, A000217, A007997, A001399, A011765 A008620, A027656, A002620, A000292, A008627.

Formula

From Sean A. Irvine, Sep 05 2022: (Start)

T(1,1) = 0.

T(n,k) = n! / (k * (n-k)) for 1 <= k < n/2.

T(2n,n) = (2*n)! / (2*n^2).

(End)

Extensions

More terms from Sean A. Irvine, Sep 05 2022