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A144280 Lower triangular array called S2hat(-3) related to partition number array A144279. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Row sums A144281.
Cf. A144275 (S2hat(-2)).
Sequence in context: A016531 A221365 A144279 * A107717 A143173 A000369
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Oct 09 2008
STATUS
approved

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Last modified October 3 19:07 EDT 2023. Contains 365870 sequences. (Running on oeis4.)