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A209573 Triangle of coefficients of polynomials u(n,x) jointly generated with A209574; see the Formula section. 3
1, 1, 1, 2, 4, 1, 3, 9, 9, 1, 4, 17, 29, 16, 1, 5, 28, 69, 74, 25, 1, 6, 42, 138, 224, 160, 36, 1, 7, 59, 245, 541, 613, 307, 49, 1, 8, 79, 399, 1127, 1781, 1469, 539, 64, 1, 9, 102, 609, 2111, 4331, 5103, 3171, 884, 81, 1, 10, 128, 884, 3649, 9281, 14419 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For n>1, let r(n,k) be the k-th number in row n.  Then

r(n,1)=n-1, r(n,n-1)=(n-1)^2, and r(n,n)=1.  For a

discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..61.

FORMULA

u(n,x)=x*u(n-1,x)+v(n-1,x),

v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

1...1

2...4....1

3...9....9....1

4...17...29...16...1

First three polynomials v(n,x): 1, 1 + x, 2 + 4x + x^2.

MATHEMATICA

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

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

v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]   (* A209573 *)

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

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

TableForm[cv]

Flatten[%]   (* A209574 *)

CROSSREFS

Cf. A209574, A208510.

Sequence in context: A208526 A275895 A158613 * A100075 A059836 A069270

Adjacent sequences:  A209570 A209571 A209572 * A209574 A209575 A209576

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 16 03:27 EDT 2019. Contains 328039 sequences. (Running on oeis4.)