A193788 Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=1+x^n.

1, 1, 1, 2, 1, 3, 4, 4, 1, 9, 8, 12, 6, 1, 27, 16, 32, 24, 8, 1, 81, 32, 80, 80, 40, 10, 1, 243, 64, 192, 240, 160, 60, 12, 1, 729, 128, 448, 672, 560, 280, 84, 14, 1, 2187, 256, 1024, 1792, 1792, 1120, 448, 112, 16, 1, 6561, 512, 2304, 4608, 5376, 4032, 2016

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..60.

Example

First six rows:
1
1....1
2....1....3
4....4....1....9
8....12...6....1...27
16...32...24...8...1...81
 (viz., A038207 with row sums at end of rows)

Mathematica

z = 10; a = 1; 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}]]  (* A193788 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193789 *)

Crossrefs

Cf. A193722, A038207, A193789.

Sequence in context: A151550 A097003 A336926 * A109447 A088261 A248393

Adjacent sequences: A193785 A193786 A193787 * A193789 A193790 A193791

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 05 2011

Status

approved