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%I #10 Aug 29 2019 15:53:01
%S 1,5,1,55,5,1,935,80,5,1,21505,1210,80,5,1,623645,29205,1335,80,5,1,
%T 21827575,782595,30580,1335,80,5,1,894930575,27002800,821095,31205,
%U 1335,80,5,1,42061737025,1058476100,27963925,827970,31205,1335,80,5,1,2229272062325,48782479625
%N Lower triangular array called S2hat(-5) related to partition number array A144341.
%C If in the partition array M32khat(-5)= A144341 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-5). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
%C The first three columns are A008543, A144344, A144345.
%H W. Lang, <a href="/A144342/a144342.txt">First 10 rows of the array and more.</a>
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL12/Lang/lang.html">Combinatorial Interpretation of Generalized Stirling Numbers</a>, J. Int. Seqs. Vol. 12 (2009) 09.3.3.
%F a(n,m)=sum(product(|S2(-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. |S2(-5,n,1)|= A013988(n,1) = A008543(n-1) = (6*n-7)(!^6) (6-factorials) for n>=2 and 1 if n=1.
%e [1];[5,1];[55,5,1];[935,80,5,1];[21505,1210,80,5,1];...
%Y Row sums A144343.
%Y A144285 (S2hat(-4)).
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_ Oct 09 2008
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