A193919 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=(x+1)^n.

1, 1, 1, 1, 3, 2, 2, 7, 9, 4, 3, 14, 25, 21, 7, 5, 28, 64, 75, 46, 12, 8, 53, 148, 224, 195, 94, 20, 13, 99, 326, 603, 679, 468, 185, 33, 21, 181, 687, 1502, 2073, 1855, 1056, 353, 54, 34, 327, 1405, 3543, 5786, 6357, 4711, 2280, 659, 88, 55, 584, 2802, 8005

Offset

0,5

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..58.

Example

First six rows:
1
1...1
1...3....2
2...7....9....4
3...14...25...21...7
5...28...64...75...46...12

Mathematica

p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := (x + 1)^n;
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}]]  (* A193919 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193920 *)

Crossrefs

Cf. A193722, A193920.

Sequence in context: A020835 A244639 A352673 * A055674 A210612 A266275

Adjacent sequences: A193916 A193917 A193918 * A193920 A193921 A193922

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 09 2011

Status

approved