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A144285
Lower triangular array called S2hat(-4) related to partition number array A144284.
6
1, 4, 1, 36, 4, 1, 504, 52, 4, 1, 9576, 648, 52, 4, 1, 229824, 12888, 712, 52, 4, 1, 6664896, 286272, 13464, 712, 52, 4, 1, 226606464, 8182944, 299520, 13720, 712, 52, 4, 1, 8837652096, 266366016, 8455392, 301824, 13720, 712, 52, 4, 1, 388856692224, 10191545280, 273091392
OFFSET
1,2
COMMENTS
If in the partition array M32khat(-4)= A144284 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-4). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
The first three columns are A008546, A144339, A144340.
FORMULA
a(n,m)=sum(product(|S2(-4;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. |S2(-4,n,1)|= A011801(n,1) = A008546(n-1) = (5*n-6)(!^5) (5-factorials) for n>=2 and 1 if n=1.
EXAMPLE
[1];[4,1];[36,4,1];[504,52,4,1];[9576,648,52,4,1];...
CROSSREFS
Row sums A144286.
A144280 (S2hat(-3)), A144342 (S2hat(-5)).
Sequence in context: A059844 A277169 A144284 * A292442 A091741 A061036
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang Oct 09 2008
STATUS
approved