A134285 Triangle of numbers obtained from the partition array A134284.

1, 3, 1, 10, 3, 1, 35, 19, 3, 1, 126, 65, 19, 3, 1, 462, 331, 92, 19, 3, 1, 1716, 1190, 421, 92, 19, 3, 1, 6435, 5587, 1805, 502, 92, 19, 3, 1, 24310, 20613, 8771, 2075, 502, 92, 19, 3, 1, 92378, 92821, 35726, 10616, 2318, 502, 92, 19, 3, 1, 352716, 347930, 160205

Offset: 1

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• nonn
• easy
• tabl

Comments

This triangle is called s2(3)'.

Examples

			Triangle starts:
1
3, 1
10, 3, 1
35, 19, 3, 1
126, 65, 19, 3, 1
...
a(4,2)=19 because the m=2 parts partitions (1^1,3^1) and (2^2) of n=4 lead to 1^1*10^1 + 3^2 =19, since A001700(n-1)=[1,3,10,...], n>=1.
		

Links

• Wolfdieter Lang, First 10 rows and more.

Crossrefs

Row sums A134826. Alternating row sums A134827.

Cf. A001700.

Formula

a(n,m) = sum(product(s2(3;j,1)^e(n,m,q,j),j=1..n),k=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;n,1) = A035324(n,1) = A001700(n-1) = binomial(2*n-1,n).

Row sums = A001700. Triangle A134285 = A001263 * A000012. - Gary W. Adamson, Nov 19 2007