A193740 Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=q(n,x) in A193738.

1, 1, 1, 1, 3, 3, 1, 4, 9, 9, 1, 4, 10, 19, 19, 1, 4, 10, 20, 34, 34, 1, 4, 10, 20, 35, 55, 55, 1, 4, 10, 20, 35, 56, 83, 83, 1, 4, 10, 20, 35, 56, 84, 119, 119, 1, 4, 10, 20, 35, 56, 84, 120, 164, 164, 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 219, 1, 4, 10, 20, 35, 56

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..71.

Example

First six rows:
1
1....1
1....3....3
1....4....9....9
1....4....10....19...19
1....4....10....20...34...34

Mathematica

z = 12;
p[0, x_] := 1
p[n_, x_] := n + Sum[(k + 1) x^(n - k), {k, 0, n - 1}]
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
t[n_, n_] := 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}]]  (* A193740 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]   (* A193741 *)

Crossrefs

Cf. A193722, A193741.

Sequence in context: A137919 A079081 A199775 * A111408 A327148 A366595

Adjacent sequences: A193737 A193738 A193739 * A193741 A193742 A193743

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 04 2011

Status

approved