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

1,2

Comments

This triangle is called s2(3)'.

Links

Table of n, a(n) for n=1..58.

Wolfdieter Lang, First 10 rows and more.

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

Example

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.

Crossrefs

Row sums A134826. Alternating row sums A134827.

Cf. A001700.

Sequence in context: A257254 A126953 A134284 * A141811 A291538 A280787

Adjacent sequences: A134282 A134283 A134284 * A134286 A134287 A134288

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Nov 13 2007

Status

approved