A193603 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A193603

Augmentation of the triangle A008949. See Comments.

1, 1, 2, 1, 5, 8, 1, 9, 30, 44, 1, 14, 77, 212, 296, 1, 20, 163, 700, 1712, 2312, 1, 27, 305, 1877, 6882, 15476, 20384, 1, 35, 523, 4365, 22380, 73240, 154424, 199376, 1, 44, 840, 9134, 62479, 280630, 841312, 1683992, 2138336

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091. The right edge of the triangle A193603 is A111537.

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

First five rows of A193603:

1...2

1...5....8

1...9...30....44

1...14...77..212...296

MATHEMATICA

p[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A008949 *)

Table[p[n, k], {n, 0, 5}, {k, 0, n}]

m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]