A193607 - OEIS

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A193607

Augmentation of the triangle A011973. See Comments.

1, 1, 1, 1, 4, 2, 1, 9, 20, 7, 1, 16, 80, 131, 37, 1, 25, 220, 806, 1085, 265, 1, 36, 490, 3130, 9360, 10952, 2402, 1, 49, 952, 9325, 48224, 124498, 130852, 26371, 1, 64, 1680, 23317, 183569, 813886, 1876101, 1809430, 340272

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

OFFSET

0,5

COMMENTS

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

(col 2): A000290 (the squares)

(col 3)= 2*A002419

LINKS

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

EXAMPLE

First five rows of A193607:

1...1

1...4....2

1...9....20...7

1...16...80...131...37

MATHEMATICA

p[n_, k_] := Binomial[2 n - k, k];

Table[p[n, k], {n, 0, 7}, {k, 0, n}] (* A011973 *)

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, 9}]] (* A193607 *)

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

CROSSREFS

Cf. A011973, A193091, A002419.

Sequence in context: A144084 A021010 A342088 * A358735 A075397 A049429

Adjacent sequences: A193604 A193605 A193606 * A193608 A193609 A193610

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved