A193604 - OEIS

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A193604

Augmentation of the triangle A055248. See Comments.

1, 2, 1, 8, 8, 3, 64, 88, 62, 19, 1024, 1664, 1568, 896, 233, 32768, 58368, 64128, 49248, 23890, 5385, 2097152, 3932160, 4703232, 4249728, 2800488, 1179656, 233787, 268435456, 517996544, 649887744, 645547008, 507802304, 293645688, 108978862

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

OFFSET

0,2

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..34.

EXAMPLE

First five rows of A193604:

2.....1

8.....8.....3

64....88....62....19

1024..1664..1568..896...233

MATHEMATICA

u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A055248 *)

p[n_, k_] := u[n, n - k]

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}]] (* A193604 *)

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

CROSSREFS

Cf. A055248, A193091.

Sequence in context: A321369 A286724 A123516 * A016446 A254794 A086657

Adjacent sequences: A193601 A193602 A193603 * A193605 A193606 A193607

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved