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A209751 Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section. 3
1, 1, 2, 2, 5, 4, 2, 10, 15, 8, 3, 14, 35, 39, 16, 3, 22, 63, 108, 95, 32, 4, 27, 109, 235, 309, 223, 64, 4, 38, 160, 454, 782, 838, 511, 128, 5, 44, 242, 770, 1688, 2408, 2183, 1151, 256, 5, 58, 322, 1264, 3226, 5776, 7009, 5512, 2559, 512, 6, 65, 450 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

v(n,x)=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...2

2...5....4

2...10...15...8

3...14...35...39...16

First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

MATHEMATICA

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

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

v[n_, 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[%]    (* A209751 *)

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

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

TableForm[cv]

Flatten[%]    (* A209752 *)

CROSSREFS

Cf. A209752, A208510.

Sequence in context: A068465 A217876 A209771 * A275381 A283235 A209763

Adjacent sequences:  A209748 A209749 A209750 * A209752 A209753 A209754

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)