|
%I #9 Aug 29 2019 15:56:46
%S 1,4,1,20,4,1,120,36,4,1,840,200,36,4,1,6720,1720,264,36,4,1,60480,
%T 12480,2040,264,36,4,1,604800,118560,16000,2296,264,36,4,1,6652800,
%U 1081920,149600,17280,2296,264,36,4,1,79833600,11793600,1362240,163680,18304,2296,264
%N Lower triangular array called S1hat(4) related to partition number array A144885.
%C If in the partition array M31hat(4):=A144885 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(4). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
%C The first columns are A001715(n+2), A144888, A144889,...
%H W. Lang, <a href="/A144886/a144886.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(|S1(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. |S1(4,n,1)|= A049352(n,1) = A001715(n+2) = (n+2)!/3!.
%e [1];[4,1];[20,4,1];[120,36,4,1];[840,200,36,4,1];...
%Y A144887 (row sums).
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_ Oct 09 2008
|
