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A193593 Augmentation of the triangle A193592.  See Comments. 2
1, 1, 1, 1, 3, 2, 1, 6, 10, 6, 1, 10, 31, 40, 23, 1, 15, 75, 166, 187, 105, 1, 21, 155, 530, 958, 993, 549, 1, 28, 287, 1415, 3786, 5988, 5865, 3207, 1, 36, 490, 3311, 12441, 28056, 40380, 37947, 20577, 1, 45, 786, 7000, 35469, 109451, 217720, 292092 (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.

Regarding A193592, (column 1)=A014616, (column 2)=A090809, (right edge)=A113227.

LINKS

Table of n, a(n) for n=0..52.

EXAMPLE

First 5 rows of A193589:

1

1...1

1...3...2

1...6...10...6

1...10..31...40...23

MATHEMATICA

p[n_, 0] := 1; p[n_, k_] := n + 1 - k /; k > 0;

Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A193592 *)

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, 12}]]  (* A193593 *)

Flatten[Table[v[n], {n, 0, 10}]]

CROSSREFS

Cf. A193091, A193592, A113227.

Sequence in context: A190909 A144250 A156367 * A181853 A008276 A094638

Adjacent sequences:  A193590 A193591 A193592 * A193594 A193595 A193596

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved

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Last modified October 22 14:53 EDT 2018. Contains 316490 sequences. (Running on oeis4.)