A134134 Triangle of numbers obtained from the partition array A134133.

1, 2, 1, 6, 2, 1, 24, 10, 2, 1, 120, 36, 10, 2, 1, 720, 204, 44, 10, 2, 1, 5040, 1104, 228, 44, 10, 2, 1, 40320, 7776, 1272, 244, 44, 10, 2, 1, 362880, 57600, 8760, 1320, 244, 44, 10, 2, 1, 3628800, 505440, 63936, 9096, 1352, 244, 44, 10, 2, 1

Offset: 1

Author

Wolfdieter Lang, Oct 12 2007

Keywords

• nonn
• easy
• tabl

Comments

In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.

Examples

			[1];[2,1];[6,2,1];[24,10,2,1];[120,36,10,2,1];...
a(4,2)=10 from the sum over the numbers related to the partitions (1,3) and (2^2), namely
1!^1*3!^1 + 2!^2 = 6+4 = 10.
		

Links

• W. Lang, First 10 rows and more.

Crossrefs

Row sums A077365. Alternating row sums A134135.

Formula

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.