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 A144285 Lower triangular array called S2hat(-4) related to partition number array A144284. 6
 1, 4, 1, 36, 4, 1, 504, 52, 4, 1, 9576, 648, 52, 4, 1, 229824, 12888, 712, 52, 4, 1, 6664896, 286272, 13464, 712, 52, 4, 1, 226606464, 8182944, 299520, 13720, 712, 52, 4, 1, 8837652096, 266366016, 8455392, 301824, 13720, 712, 52, 4, 1, 388856692224, 10191545280, 273091392 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If in the partition array M32khat(-4)= A144284 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-4). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040. The first three columns are A008546, A144339, A144340. 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(|S2(-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 and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S2(-4,n,1)|= A011801(n,1) = A008546(n-1) = (5*n-6)(!^5) (5-factorials) for n>=2 and 1 if n=1. EXAMPLE [1];[4,1];[36,4,1];[504,52,4,1];[9576,648,52,4,1];... CROSSREFS Row sums A144286. A144280 (S2hat(-3)), A144342 (S2hat(-5)). Sequence in context: A059844 A277169 A144284 * A292442 A091741 A061036 Adjacent sequences:  A144282 A144283 A144284 * A144286 A144287 A144288 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang Oct 09 2008 STATUS approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)