A193899 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=x*p(n-1,x)+2^n, p(0,x)=1.

1, 1, 2, 2, 5, 10, 4, 10, 21, 42, 8, 20, 42, 85, 170, 16, 40, 84, 170, 341, 682, 32, 80, 168, 340, 682, 1365, 2730, 64, 160, 336, 680, 1364, 2730, 5461, 10922, 128, 320, 672, 1360, 2728, 5460, 10922, 21845, 43690, 256, 640, 1344, 2720, 5456, 10920

Offset

0,3

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..50.

Example

First six rows of A193897:
1
1....2
2....5....10
4....10...21...42
8....20...42...85....170
16...40...84...170...341...682

Mathematica

z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := p[n, x];
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}]]  (* A193899 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193900 *)

Crossrefs

Cf. A193722, A193900.

Sequence in context: A110182 A309867 A304584 * A334017 A208567 A273968

Adjacent sequences: A193896 A193897 A193898 * A193900 A193901 A193902

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved