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A209575 Triangle of coefficients of polynomials u(n,x) jointly generated with A209576; see the Formula section. 3
1, 1, 1, 1, 5, 1, 1, 5, 15, 1, 1, 5, 23, 37, 1, 1, 5, 23, 89, 83, 1, 1, 5, 23, 105, 295, 177, 1, 1, 5, 23, 105, 447, 873, 367, 1, 1, 5, 23, 105, 479, 1721, 2383, 749, 1, 1, 5, 23, 105, 479, 2121, 6015, 6137, 1515, 1, 1, 5, 23, 105, 479, 2185, 8847, 19369, 15143 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

1...5...1

1...5...15...1

1...5...23...37...1

First three polynomials v(n,x): 1, 1 + x, 1 + 5x + 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] + 2 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[%]   (* A209575 *)

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

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

TableForm[cv]

Flatten[%]   (* A209576 *)

CROSSREFS

Cf. A209576, A208510.

Sequence in context: A071856 A242133 A144221 * A159570 A280374 A259975

Adjacent sequences:  A209572 A209573 A209574 * A209576 A209577 A209578

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)