A145364 Lower triangular array, called S1hat(-2), related to partition number array A145363.

1, 2, 1, 2, 2, 1, 0, 6, 2, 1, 0, 4, 6, 2, 1, 0, 4, 12, 6, 2, 1, 0, 0, 12, 12, 6, 2, 1, 0, 0, 8, 28, 12, 6, 2, 1, 0, 0, 8, 24, 28, 12, 6, 2, 1, 0, 0, 0, 24, 56, 28, 12, 6, 2, 1, 0, 0, 0, 16, 56, 56, 28, 12, 6, 2, 1, 0, 0, 0, 16, 48, 120, 56, 28, 12, 6, 2, 1, 0, 0, 0, 0, 48, 112, 120, 56, 28, 12, 6, 2, 1

Offset

1,2

Comments

If in the partition array M31hat(-2):=A145363 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-2). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first column is [1,2,2,0,0,0,...]= A008279(2,n-1), n>=1.

Links

Table of n, a(n) for n=1..91.

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(product(S1(-2;j,1)^e(n,m,q,j),j=1..n),q=1..p(n,m)) 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. S1(-2,n,1)= A008279(2,n-1) = [1,2,2,0,0,0,...], n>=1.

Example

Triangle begins:
  [1];
  [2,1];
  [2,2,1];
  [0,6,2,1];
  [0,4,6,2,1];
  ...

Crossrefs

Cf. A145365 (row sums).

Sequence in context: A145363 A071429 A264398 * A284978 A175862 A261083

Adjacent sequences: A145361 A145362 A145363 * A145365 A145366 A145367

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Oct 17 2008

Status

approved