login
A145373
Lower triangular array, called S1hat(-5), related to partition number array A145372.
3
1, 5, 1, 20, 5, 1, 60, 45, 5, 1, 120, 160, 45, 5, 1, 120, 820, 285, 45, 5, 1, 0, 1920, 1320, 285, 45, 5, 1, 0, 6600, 5420, 1945, 285, 45, 5, 1, 0, 9600, 23600, 7920, 1945, 285, 45, 5, 1, 0, 21600, 66600, 41100, 11045, 1945, 285, 45, 5, 1, 0, 14400, 189600, 151600, 53600, 11045
OFFSET
1,2
COMMENTS
If in the partition array M31hat(-5):=A145372 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-5). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first column is [1,5,20,60,120,120,0,0,0,...]= A008279(5,n-1), n>=1.
FORMULA
a(n,m)=sum(product(S1(-5;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(-5,n,1)= A008279(5,n-1) = [1,5,20,60,120,120,0,0,0,...], n>=1.
EXAMPLE
[1];[5,1];[20,5,1];[60,45,5,1];[120,160,45,5,1];...
CROSSREFS
A145374 (row sums).
Sequence in context: A066480 A136394 A145372 * A088577 A368380 A127561
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang Oct 17 2008
STATUS
approved