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

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

W. Lang, First 10 rows and more.

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.

Example

[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.

Crossrefs

Row sums A077365. Alternating row sums A134135.

Sequence in context: A134133 A157392 A321352 * A222005 A351442 A325815

Adjacent sequences: A134131 A134132 A134133 * A134135 A134136 A134137

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Oct 12 2007

Status

approved