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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A293268 A020835 A244639 * A210612 A055674 A266275

Adjacent sequences:  A193916 A193917 A193918 * A193920 A193921 A193922

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 09 2011

STATUS

approved

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Last modified June 4 17:13 EDT 2020. Contains 334828 sequences. (Running on oeis4.)