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A209705 Triangle of coefficients of polynomials u(n,x) jointly generated with A209706; see the Formula section. 4
1, 0, 2, 0, 3, 4, 0, 4, 10, 8, 0, 5, 18, 28, 16, 0, 6, 28, 64, 72, 32, 0, 7, 40, 120, 200, 176, 64, 0, 8, 54, 200, 440, 576, 416, 128, 0, 9, 70, 308, 840, 1456, 1568, 960, 256, 0, 10, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 0, 11, 108, 624, 2352, 6048 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternating row sums: 1,-2,1,-2,1,-2,1,-2,...

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

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

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

T(n,k) = 2*T(n-1,k)+2*T(n-1,k-1)-T(n-2,k)-2*T(n-2,k-1), T(1,0)=1, T(2,0)=0, T(2,1)=2, T(3,0)=0, T(3,1)=3, T(3,2)=4, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Dec 27 2013

EXAMPLE

First five rows:

1

0...2

0...3...4

0...4...10...8

0...5...18...28...16

First three polynomials v(n,x): 1, 2x, 3x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]  (* A209705 *)

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

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

TableForm[cv]

Flatten[%]  (* A209706 *)

CROSSREFS

Cf. A209706, A208510.

Sequence in context: A099091 A227595 A078436 * A181289 A229032 A117909

Adjacent sequences:  A209702 A209703 A209704 * A209706 A209707 A209708

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified December 14 09:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)