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A144351 Lower triangular array called S1hat(1) related to partition number array A107106. 2
1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 8, 3, 1, 1, 120, 34, 9, 3, 1, 1, 720, 156, 36, 9, 3, 1, 1, 5040, 924, 166, 37, 9, 3, 1, 1, 40320, 6144, 968, 168, 37, 9, 3, 1, 1, 362880, 48096, 6372, 978, 169, 37, 9, 3, 1, 1, 3628800, 420480, 49368, 6416, 980, 169, 37, 9, 3, 1, 1, 39916800, 4134240 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

If in the partition array M31hat(1):=A107106 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(1). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first three columns are A000142(n-1) (factorials), A024419 (guess), A144352.

LINKS

Table of n, a(n) for n=1..68.

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

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

FORMULA

a(n,m)=sum(product(|S1(1;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(1,n,1)|= |A008275(n,1)| = A000142(n-1) = (n-1)!.

EXAMPLE

[1];[1,1];[2,1,1];[6,3,1,1];[24,8,3,1,1];...

CROSSREFS

Row sums A107107.

A134134 (S1hat(2)= S2'(2)).

Sequence in context: A120258 A201922 A181644 * A213936 A142589 A284308

Adjacent sequences:  A144348 A144349 A144350 * A144352 A144353 A144354

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang Oct 09 2008

STATUS

approved

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Last modified June 18 16:26 EDT 2021. Contains 345120 sequences. (Running on oeis4.)