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A193792 Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(x+3)^n and q(n,x)=1+x^n. 2
1, 1, 1, 3, 1, 4, 9, 6, 1, 16, 27, 27, 9, 1, 64, 81, 108, 54, 12, 1, 256, 243, 405, 270, 90, 15, 1, 1024, 729, 1458, 1215, 540, 135, 18, 1, 4096, 2187, 5103, 5103, 2835, 945, 189, 21, 1, 16384, 6561, 17496, 20412, 13608, 5670, 1512, 252, 24, 1, 65536 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

First six rows:

1

1....1

3....1....4

9....6....1....16

27...27...9....1...64

81...108..54...12..1...256

MATHEMATICA

z = 8; a = 1; b = 3;

p[n_, x_] := (a*x + b)^n

q[n_, x_] := 1 + x^n ; q[n_, 0] := q[n, x] /. x -> 0;

t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

g[n_] := CoefficientList[w[n, x], {x}]

TableForm[Table[Reverse[g[n]], {n, -1, z}]]

Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193792 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193793 *)

CROSSREFS

Cf. A193722, A193733.

Sequence in context: A338871 A202353 A108621 * A190179 A025116 A178300

Adjacent sequences:  A193789 A193790 A193791 * A193793 A193794 A193795

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 05 2011

STATUS

approved

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Last modified August 15 12:09 EDT 2022. Contains 356145 sequences. (Running on oeis4.)