A145364 - OEIS

%I #10 Aug 29 2019 17:13:02

%S 1,2,1,2,2,1,0,6,2,1,0,4,6,2,1,0,4,12,6,2,1,0,0,12,12,6,2,1,0,0,8,28,

%T 12,6,2,1,0,0,8,24,28,12,6,2,1,0,0,0,24,56,28,12,6,2,1,0,0,0,16,56,56,

%U 28,12,6,2,1,0,0,0,16,48,120,56,28,12,6,2,1,0,0,0,0,48,112,120,56,28,12,6,2,1

%N Lower triangular array, called S1hat(-2), related to partition number array A145363.

%C If in the partition array M31hat(-2):=A145363 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(-2). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

%C The first column is [1,2,2,0,0,0,...]= A008279(2,n-1), n>=1.

%H W. Lang, <a href="/A145364/a145364.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(-2;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(-2,n,1)= A008279(2,n-1) = [1,2,2,0,0,0,...], n>=1.

%e [1];[2,1];[2,2,1];[0,6,2,1];[0,4,6,2,1];...

%Y A145365 (row sums).

%K nonn,easy,tabl

%O 1,2

%A _Wolfdieter Lang_ Oct 17 2008