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.

1, 1, 1, 2, 3, 5, 4, 12, 9, 25, 8, 36, 54, 27, 125, 16, 96, 216, 216, 81, 625, 32, 240, 720, 1080, 810, 243, 3125, 64, 576, 2160, 4320, 4860, 2916, 729, 15625, 128, 1344, 6048, 15120, 22680, 20412, 10206, 2187, 78125, 256, 3072, 16128, 48384, 90720

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..49.

Example

First six rows:
1
1....1
2....3....5
4....12...9.....25
8....36...54....27...125
16...96...216...216..81...625

Mathematica

z = 8; a = 3; b = 2;
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}]]  (* A193798 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193799 *)

Crossrefs

Cf. A193722, A193799.

Sequence in context: A023395 A316655 A318848 * A101409 A271862 A309373

Adjacent sequences: A193795 A193796 A193797 * A193799 A193800 A193801

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved