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A145370
Lower triangular array, called S1hat(-4), related to partition number array A145369.
4
1, 4, 1, 12, 4, 1, 24, 28, 4, 1, 24, 72, 28, 4, 1, 0, 264, 136, 28, 4, 1, 0, 384, 456, 136, 28, 4, 1, 0, 864, 1344, 712, 136, 28, 4, 1, 0, 576, 4128, 2112, 712, 136, 28, 4, 1, 0, 576, 7488, 7968, 3136, 712, 136, 28, 4, 1, 0, 0, 13248, 20544, 11040, 3136, 712, 136, 28, 4, 1, 0, 0
OFFSET
1,2
COMMENTS
If in the partition array M31hat(-4):=A145369 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-4). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first column is [1,4,12,24,24,0,0,0,...]= A008279(4,n-1), n>=1.
FORMULA
a(n,m)=sum(product(S1(-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, Y and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. S1(-4,n,1)= A008279(4,n-1) = [1,4,12,24,24,0,0,0,...], n>=1.
EXAMPLE
[1];[4,1];[12,4,1];[24,28,4,1];[24,72,28,4,1];...
CROSSREFS
A145371 (row sums).
Sequence in context: A175763 A080303 A145369 * A130322 A316232 A372354
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang Oct 17 2008
STATUS
approved