AUTHOR
_Clark Kimberling (ck6(AT)evansville.edu), _, Aug 05 2011
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Revision History for A193796
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Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+3)^n and q(n,x)=1+x^n.
(history; published version)
(history; published version)
STATUS
proposed
approved
STATUS
editing
proposed
NAME
allocated for Clark KimberlingTriangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+3)^n and q(n,x)=1+x^n.
DATA
1, 1, 1, 3, 2, 5, 9, 12, 4, 25, 27, 54, 36, 8, 125, 81, 216, 216, 96, 16, 625, 243, 810, 1080, 720, 240, 32, 3125, 729, 2916, 4860, 4320, 2160, 576, 64, 15625, 2187, 10206, 20412, 22680, 15120, 6048, 1344, 128, 78125, 6561, 34992, 81648, 108864, 90720
OFFSET
0,4
COMMENTS
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
EXAMPLE
First six rows:
1
1....1
3....2....5
9....12...4....25
27...54...36...8...125
81...216..216..96..16...625
MATHEMATICA
z = 8; a = 2; 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}]] (* A193796 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193797 *)
KEYWORD
allocated
nonn,tabl
AUTHOR
Clark Kimberling (ck6(AT)evansville.edu), Aug 05 2011
STATUS
approved
editing
NAME
allocated for Clark Kimberling
KEYWORD
allocated
STATUS
approved