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A133567 A007318 * A133566. 4
1, 1, 1, 1, 3, 1, 1, 6, 3, 1, 1, 10, 6, 5, 1, 1, 15, 10, 15, 5, 1, 1, 21, 15, 35, 15, 7, 1, 1, 28, 21, 70, 35, 28, 7, 1, 1, 36, 28, 126, 70, 84, 28, 9, 1, 1, 45, 36, 210, 126, 210, 84, 45, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums = A083329: (1, 2, 5, 11, 23, 47, 95,...).

From Clark Kimberling, Feb 28 2012 (start):

A133567 is jointly generated with A133084 as an array of coefficients of polynomials v(n,x): initially, u(1,x)=v(1,x)=1; for n>1, u(n,x)=u(n-1,x)+(x+1)*v(n-1)x and v(n,x)=x*u(n-1,x)+v(n-1,x)+1.  See the Mathematica section.

(end)

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Binomial transform of triangle A133566.

EXAMPLE

First few rows of the triangle are;

1;

1, 1;

1, 3, 1;

1, 6, 3, 1;

1, 10, 6, 5, 1;

1, 15, 10, 15, 5, 1;

1, 21, 15, 35, 15, 7, 1;

...

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A133567 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]  (* A133084 *)

(* Clark Kimberling, Feb 28 2012 *)

CROSSREFS

Cf. A133566, A083329, A133084.

Sequence in context: A275464 A067433 A256697 * A271665 A184049 A125230

Adjacent sequences:  A133564 A133565 A133566 * A133568 A133569 A133570

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 16 2007

STATUS

approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)