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A193607 Augmentation of the triangle A011973.  See Comments. 2
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

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 * A075397 A049429 A328647

Adjacent sequences:  A193604 A193605 A193606 * A193608 A193609 A193610

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved

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Last modified April 17 20:39 EDT 2021. Contains 343070 sequences. (Running on oeis4.)