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%I #10 Aug 28 2019 16:59:55
%S 1,2,1,6,2,1,24,10,2,1,120,36,10,2,1,720,204,44,10,2,1,5040,1104,228,
%T 44,10,2,1,40320,7776,1272,244,44,10,2,1,362880,57600,8760,1320,244,
%U 44,10,2,1,3628800,505440,63936,9096,1352,244,44,10,2,1
%N Triangle of numbers obtained from the partition array A134133.
%C In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.
%H W. Lang, <a href="/A134134/a134134.txt">First 10 rows and more</a>.
%F a(n,m)=sum(product(j!^e(n,m,k,j),j=1..n),k=1..p(n,m)) if n>=m>=1, else 0, with p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,k,j) is the exponent of j in the k-th m part partition of n.
%e [1];[2,1];[6,2,1];[24,10,2,1];[120,36,10,2,1];...
%e a(4,2)=10 from the sum over the numbers related to the partitions (1,3) and (2^2), namely
%e 1!^1*3!^1 + 2!^2 = 6+4 = 10.
%Y Row sums A077365. Alternating row sums A134135.
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_, Oct 12 2007
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