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A144270
Lower triangular array called S2hat(-1) related to partition number array A144269.
6
1, 1, 1, 3, 1, 1, 15, 4, 1, 1, 105, 18, 4, 1, 1, 945, 129, 19, 4, 1, 1, 10395, 1095, 132, 19, 4, 1, 1, 135135, 11880, 1119, 133, 19, 4, 1, 1, 2027025, 149940, 12057, 1122, 133, 19, 4, 1, 1, 34459425, 2218545, 151560, 12081, 1123, 133, 19, 4, 1, 1
OFFSET
1,4
COMMENTS
If in the partition array M32hat(-1)=A144269 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-1). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
The first three columns are A001147, A144272, A144273.
LINKS
FORMULA
a(n,m)=sum(product(|S2(-1;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(-1;j,1)|= A001497(j-1,0) = A001147(j-1) = (2*j-3)(!^2) (2-factorials) for j>=2 and 1 if j=1.
EXAMPLE
Triangle begins
1;
1, 1;
3, 1, 1;
15, 4, 1, 1;
105, 18, 4, 1, 1;
...
CROSSREFS
Row sums A144271.
Sequence in context: A006956 A072285 A144269 * A110112 A370691 A326800
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Oct 09 2008
STATUS
approved