A193796 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.

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.

Links

Table of n, a(n) for n=0..49.

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 *)

Crossrefs

Cf. A193722, A193797.

Sequence in context: A257705 A257878 A243700 * A249906 A258930 A002797

Adjacent sequences: A193793 A193794 A193795 * A193797 A193798 A193799

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved