0,5

By columns, going right from the triangular numbers: A006522 = (1,4,11,25...), then A055796, A002663, A002664, A035038. Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320...). A125231 also generates the same row sums.

Binomial transform of an infinite matrix M with k consecutive 1's in the k-th column (headings 1,2,3...), prefaced with (n-1) consecutive 0's; and the rest zeros. First few columns of M are: (1,0,0,0...), (0,1,1,0,0,0...), (0,0,1,1,1,0,0,0...); etc.

First few rows of the triangle are:

1;

1, 1;

1, 3, 1;

1, 6, 4, 1;

1, 10, 11, 5, 1;

1, 15, 25, 16, 6, 1;

1, 21, 50, 42, 22, 7, 1;

1, 28, 91, 98, 64, 29, 8, 1;

...

Cf. A045623, A006522, A055796, A002663, A002664, A035038.

Sequence in context: A061857 A067433 A133567 this_sequence A128101 A124802 A102036

Adjacent sequences: A125227 A125228 A125229 this_sequence A125231 A125232 A125233

nonn,tabl,uned

Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 24 2006