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

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• nonn
• easy
• tabl

Comments

This triangle is named S2(3)'.

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

Examples

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

Links

• W. Lang, First 10 rows and more.

Crossrefs

Cf. A134147 (row sums).

Cf. A134148 (allternating row sums).

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

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)!!.