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

1,3

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.

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

Table of n, a(n) for n=1..38.

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].

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)

Example

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

Crossrefs

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

Sequence in context: A146975 A046970 A322360 * A280369 A280979 A281045

Adjacent sequences: A058933 A058934 A058935 * A058937 A058938 A058939

Keyword

nonn,tabf

Author

Alford Arnold, Jan 11 2001

Extensions

More terms from Sean A. Irvine, Sep 05 2022

Status

approved