A139687 Basis of degenerate cases of sequences identical to its p-th differences. Complement to A140344 which is based on natural Catalan's triangle. Triangle without first term (probable 1) on line.

1, 1, 1, 2, 2, 1, 3, 5, 5, 1, 3, 6, 9, 9, 1, 4, 10, 19, 28, 28, 1, 4, 10, 20, 34, 48, 48, 1, 5, 15, 35, 69, 117, 165, 165, 1, 5, 15, 35, 70, 125, 200, 275, 275, 1, 6, 21, 56, 126, 251, 451, 726, 1001, 1001, 1, 6, 21, 56, 126, 252, 461, 780, 1209, 1638, 1638

Offset: 0

Author

Paul Curtz, Jun 13 2008

Keywords

• nonn
• uned

Comments

Triangle from A140344:

(1;)

0, 1, 1;

0, 0, 1, 2, 2;

0, 0, 0, 1, 3, 5, 5; see A138112,

0, 0, 0, 0, 1, 4, 9, 14, 14; see A140343,

begins (without 0's) like a(n).

Crossrefs

Cf. A135356, A140344.

Formula

First four rows of triangle from second row: 1, 1; 1, 2, 2; see A099087, 1, 3, 5, 5; 1, 3, 6, 9, 9; see A057083 which can be preceded with 3 leading 0's, are, as said, from natural Catalan's triangle A009766. Origin of a(n) explained later.