A134275 Triangle of numbers obtained from the partition array A134274.

1, 5, 1, 45, 5, 1, 585, 70, 5, 1, 9945, 810, 70, 5, 1, 208845, 14895, 935, 70, 5, 1, 5221125, 284895, 16020, 935, 70, 5, 1, 151412625, 7055100, 309645, 16645, 935, 70, 5, 1, 4996616625, 192734100, 7526475, 315270, 16645, 935, 70, 5, 1, 184874815125

Offset

1,2

Comments

This triangle is named S2(5)'.

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..46.

Wolfdieter Lang, First 10 rows and more.

Formula

a(n,m) = sum(product(S2(5;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(5;j,1)= A007696(j) = A049029(j,1) = (4*j-3)(!^4), (quadruple- or 4-factorials).

Example

Triangle begins:
  [1];
  [5,1];
  [45,5,1];
  [585,70,5,1];
  [9945,810,70,5,1];
  ...

Crossrefs

Cf. A134276 (row sums). A134277 (alternating row sums).

Cf. A134151 (S2(4)').

Sequence in context: A269910 A221366 A134274 * A264774 A114154 A297899

Adjacent sequences: A134272 A134273 A134274 * A134276 A134277 A134278

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Nov 13 2007

Status

approved