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A145357 Lower triangular array, called S1hat(6), related to partition number array A145356. 5
1, 6, 1, 42, 6, 1, 336, 78, 6, 1, 3024, 588, 78, 6, 1, 30240, 6804, 804, 78, 6, 1, 332640, 62496, 8316, 804, 78, 6, 1, 3991680, 753984, 85176, 9612, 804, 78, 6, 1, 51891840, 8273664, 1021608, 94248, 9612, 804, 78, 6, 1, 726485760, 109118016, 11394432, 1157688, 102024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If in the partition array M31hat(6):=A145356 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(6). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first columns are A001725(n+4), A145359, A145360,...
LINKS
W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.
FORMULA
a(n,m)=sum(product(|S1(6;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(6,n,1)|= A049374(n,1) = A001725(n+4) = (n+4)!/5!.
EXAMPLE
[1];[6,1];[42,6,1];[336,78,6,1];[3024,588,78,6,1];...
CROSSREFS
A145358(row sums).
Sequence in context: A113365 A293172 A145356 * A035529 A135893 A051338
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang Oct 17 2008
STATUS
approved

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Last modified May 26 19:24 EDT 2024. Contains 372844 sequences. (Running on oeis4.)