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A134134 Triangle of numbers obtained from the partition array A134133. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A325815 A292441

Adjacent sequences:  A134131 A134132 A134133 * A134135 A134136 A134137

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Oct 12 2007

STATUS

approved

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)