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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 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..55.

W. Lang, First 10 rows of the array and more.

W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.

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

[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 A326800 A176225

Adjacent sequences:  A144267 A144268 A144269 * A144271 A144272 A144273

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang Oct 09 2008

STATUS

approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)