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

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
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}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193603 *)
Flatten[Table[v[n], {n, 0, 8}]]

Crossrefs

Cf. A008949, A193091, A111537.

Sequence in context: A175770 A268950 A141507 * A059274 A082635 A166623

Adjacent sequences: A193600 A193601 A193602 * A193604 A193605 A193606

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 31 2011

Status

approved