1,4

Calculating the appropriate weights can be done by "working backward". Suppose, for example we know the weights for 1 through 6 and desire the weight for the partitions of seven: Substitute the weights for each partition value and multiply. For example, 7 = 4+3 so f[4,3] = 6*2 = 12; adjusting for the number of permutations of {4,3] we now have 2*12 = 24 Bells. Continuing in this manner for each partition of seven and summing to 451 we now know all of the Bell values except the value associated with the partition "7" which must be 877-451 = 426.

Subtriangle (n>=1 and 1<=k<=n} of triangle given by [0,1,1,2,1,3,1,4,1,5,1,6,...] DELTA [1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 03 2007

The partitions of 4 are

4 31 22 211 1111

the Bells are

6 4 1 3 1

therefore row 4 of the table is

6 5 3 1

Comment from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 03 2007: Triangle begins:

1;

1, 1;

2, 2, 1;

6, 5, 3, 1;

22, 16, 9, 4, 1;

92, 60, 31, 14, 5, 1;

426, 252, 120, 52, 20, 6, 1;

2146, 1160, 510, 209, 80, 27, 7, 1 ;...

Triangle [0,1,1,2,1,3,1,4,1,...] DELTA [1,0,0,0,0,0,...] begins:

1;

0, 1;

0, 1, 1;

0, 2, 2, 1;

0, 6, 5, 3, 1;

0, 22, 16, 9, 4, 1;

0, 92, 60, 31, 14, 5, 1;

0, 426, 252, 120, 52, 20, 6, 1;

0, 2146, 1160, 510, 209, 80, 27, 7, 1 ;...

Cf. A000041 A000110 A036043 A036042 A084938.

Sequence in context: A106381 A064784 A108074 this_sequence A125278 A134558 A137381

Adjacent sequences: A127740 A127741 A127742 this_sequence A127744 A127745 A127746

nonn,tabl,uned

Alford Arnold (Alford1940(AT)aol.com), Feb 24 2007