This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193798 Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=(3x+2)^n and q(n,x)=1+x^n. 2

%I

%S 1,1,1,2,3,5,4,12,9,25,8,36,54,27,125,16,96,216,216,81,625,32,240,720,

%T 1080,810,243,3125,64,576,2160,4320,4860,2916,729,15625,128,1344,6048,

%U 15120,22680,20412,10206,2187,78125,256,3072,16128,48384,90720

%N Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(3x+2)^n and q(n,x)=1+x^n.

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

%e First six rows:

%e 1

%e 1....1

%e 2....3....5

%e 4....12...9.....25

%e 8....36...54....27...125

%e 16...96...216...216..81...625

%t z = 8; a = 3; b = 2;

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

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

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

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

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

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

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193798 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193799 *)

%Y Cf. A193722, A193799.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 05 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified June 18 22:35 EDT 2013. Contains 226356 sequences.