A144275 Lower triangular array called S2hat(-2) related to partition number array A144274.

1, 2, 1, 10, 2, 1, 80, 14, 2, 1, 880, 100, 14, 2, 1, 12320, 1140, 108, 14, 2, 1, 209440, 14880, 1180, 108, 14, 2, 1, 4188800, 249280, 15400, 1196, 108, 14, 2, 1, 96342400, 4801280, 255400, 15480, 1196, 108, 14, 2, 1, 2504902400, 108574400, 4888960, 256440, 15512

Offset

1,2

Comments

If in the partition array M32khat(-2)= A144274 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-2). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.

The first three columns are A008544, A144277, A144278.

Links

Table of n, a(n) for n=1..50.

Wolfdieter Lang, First 10 rows of the array and more.

Wolfdieter Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.

Formula

a(n,m) = Sum_{q=1..p(n,m)} (Product_{j=1..n} |S2(-2;j,1)|^e(n,m,q,j)) if n>=m>=1, else 0. Here p(n,m) = A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S2(-2,n,1)|= A004747(n,1) = A008544(n-1) = (3*n-4)(!^3) (3-factorials) for n>=2 and 1 if n=1.

Example

Triangle begins:
  [1];
  [2,1];
  [10,2,1];
  [80,14,2,1];
  [880,100,14,2,1];
  ...

Crossrefs

Row sums A144276.

A144270 (S2hat(-1)).

Cf. A004747, A008284, A008544.

Sequence in context: A112691 A110169 A144274 * A247236 A011268 A332080

Adjacent sequences: A144272 A144273 A144274 * A144276 A144277 A144278

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Oct 09 2008

Status

approved