A144280 Lower triangular array called S2hat(-3) related to partition number array A144279.

1, 3, 1, 21, 3, 1, 231, 30, 3, 1, 3465, 294, 30, 3, 1, 65835, 4599, 321, 30, 3, 1, 1514205, 81081, 4788, 321, 30, 3, 1, 40883535, 1837836, 84483, 4869, 321, 30, 3, 1, 1267389585, 47609100, 1892835, 85050, 4869, 321, 30, 3, 1, 44358635475, 1449052605, 48681864

Offset

1,2

Comments

If in the partition array M32khat(-3)= A144279 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-3). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.

The first three columns are A008545, A144282, A144283.

Links

Table of n, a(n) for n=1..48.

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(-3;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(-3,n,1)|= A000369(n,1) = A008545(n-1) = (4*n-5)(!^4) (4-factorials) for n>=2 and 1 if n=1.

Example

Triangle begins:
  [1];
  [3,1];
  [21,3,1];
  [231,30,3,1];
  [3465,294,30,3,1];
  ...

Crossrefs

Cf. A144279, A008277, A036040, A008284, A000369, A008545, A144282, A144283.

Row sums A144281.

Cf. A144275 (S2hat(-2)).

Sequence in context: A016531 A221365 A144279 * A107717 A143173 A000369

Adjacent sequences: A144277 A144278 A144279 * A144281 A144282 A144283

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Oct 09 2008

Status

approved