A134146 Triangle of numbers obtained from the partition array A134145.

1, 3, 1, 15, 3, 1, 105, 24, 3, 1, 945, 150, 24, 3, 1, 10395, 1485, 177, 24, 3, 1, 135135, 14805, 1620, 177, 24, 3, 1, 2027025, 191520, 16425, 1701, 177, 24, 3, 1, 34459425, 2687580, 208125, 16830, 1701, 177, 24, 3, 1, 654729075, 44552025, 2880360, 212985

Offset

1,2

Comments

This triangle is named S2(3)'.

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..49.

W. Lang, First 10 rows and more.

Formula

a(n,m)=sum(product(S2(3;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(3;j,1)= A001147(j) = A035342(j,1) = (2*j-1)!!.

Example

[1]; [3,1]; [15,3,1]; [105,24,3,1]; [945,150,24,3,1];...

Crossrefs

Cf. A134147 (row sums).

Cf. A134148 (allternating row sums).

Cf. A134134 (k=2 member of this triangle family).

Sequence in context: A108083 A163239 A134145 * A085569 A336454 A261671

Adjacent sequences: A134143 A134144 A134145 * A134147 A134148 A134149

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Nov 13 2007

Status

approved