1,5

Rows of the array tend to the Catalan sequence, A000108 starting (1, 2, 5, 14, 42,...).

Antidiagonals of an array formed by A000012 * A001263(transform), as infinite triangular matrices. A000012 = (1; 1,1; 1,1,1; 1,1,1,1;...), A001263 = the Narayana triangle.

First few rows of the array are:

1,...1,....1,....1,....1,...

1,...2,....4,....7,...11,...

1,...2,....5,...13,...31,...

1,...2,....5,...14,...41,...

1,...2,....5,...14,...42,...

...

First few rows of the triangle are:

1;

1, 1;

1, 2, 1;

1, 2, 4, 1;

1, 2, 5, 7, 1;

1, 2, 5, 13, 11, 1;

1, 2, 5, 14, 31, 16, 1;

1, 2, 5, 14, 41, 66, 22, 1;

1, 2, 5, 14, 42, 116, 127, 29, 1;

1, 2, 5, 14, 42, 131, 302, 225, 37, 1;

1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1;

...

Cf. A001263, A000108.

Sequence in context: A140994 A140993 A027935 this_sequence A137855 A113143 A136788

Adjacent sequences: A137937 A137938 A137939 this_sequence A137941 A137942 A137943

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 24 2008