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A193601 Augmentation of the triangle A062344.  See Comments. 1
1, 1, 2, 1, 6, 10, 1, 12, 49, 76, 1, 20, 149, 508, 756, 1, 30, 354, 2082, 6353, 9192, 1, 42, 720, 6484, 32852, 92750, 131406, 1, 56, 1315, 16820, 127365, 580606, 1545757, 2153912, 1, 72, 2219, 38256, 404559, 2706150, 11385058, 28931758, 39768798 (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.

LINKS

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

EXAMPLE

First 5 rows of A193601:

1

1...2

1...6....10

1...12...49...76

1...20...149..508...756

MATHEMATICA

p[n_, k_] := Binomial[2 n, k] (* A062344 *)

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}]] (* A193601 *)

Flatten[Table[v[n], {n, 0, 8}]]

CROSSREFS

Cf. A193091, A062344.

Sequence in context: A160565 A025252 A177863 * A157402 A069114 A173773

Adjacent sequences:  A193598 A193599 A193600 * A193602 A193603 A193604

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)