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 A144891 Lower triangular array called S1hat(5) related to partition number array A144890. 5
 1, 5, 1, 30, 5, 1, 210, 55, 5, 1, 1680, 360, 55, 5, 1, 15120, 3630, 485, 55, 5, 1, 151200, 29820, 4380, 485, 55, 5, 1, 1663200, 321300, 39570, 5005, 485, 55, 5, 1, 19958400, 3225600, 421800, 43320, 5005, 485, 55, 5, 1, 259459200, 38808000, 4265100, 470550, 46445, 5005 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If in the partition array M31hat(5):=A144890 entries 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 columns are A001720(n+3)=(n+3)!/4!, A144893, A144894,... LINKS 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(|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)|= A049353(n,1) = A001720(n+3) = (n+3)!/4!. EXAMPLE [1];[5,1];[30,5,1];[210,55,5,1];[1680,360,55,5,1];... CROSSREFS A144892 (row sums). Sequence in context: A232015 A214882 A144890 * A135892 A049460 A145926 Adjacent sequences:  A144888 A144889 A144890 * A144892 A144893 A144894 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang Oct 09 2008 STATUS approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)