A134151 Triangle of numbers obtained from the partition array A134150.

1, 4, 1, 28, 4, 1, 280, 44, 4, 1, 3640, 392, 44, 4, 1, 58240, 5544, 456, 44, 4, 1, 1106560, 80640, 5992, 456, 44, 4, 1, 24344320, 1519840, 88256, 6248, 456, 44, 4, 1, 608608000, 31420480, 1631392, 90048, 6248, 456, 44, 4, 1, 17041024000, 766525760, 33293120

Offset

1,2

Comments

This triangle is named S2(4)'.

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..48.

W. Lang, First 10 rows and more.

Formula

a(n,m)=sum(product(S2(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. S2(4;j,1)= A007559(j) = A035469(j,1) = (3*j-2)!!!.

Example

[1]; [4,1]; [28,4,1]; [280,44,4,1]; [3640,392,44,4,1];...

Crossrefs

Cf. A134152 (row sums). A134272 (alternating row sums).

Cf. A134146 (S2(3)' triangle).

Sequence in context: A096206 A336913 A134150 * A264773 A119304 A114150

Adjacent sequences: A134148 A134149 A134150 * A134152 A134153 A134154

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Nov 13 2007

Status

approved