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A207627 Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section. 3
1, 2, 3, 4, 4, 10, 8, 5, 18, 28, 16, 6, 28, 64, 72, 32, 7, 40, 120, 200, 176, 64, 8, 54, 200, 440, 576, 416, 128, 9, 70, 308, 840, 1456, 1568, 960, 256, 10, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 11, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column n is divisible by 2^(n-1); row n ends with 2^(n-1).

LINKS

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

FORMULA

u(n,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.

The row sums =:  2, 7, 22, 67, ... are given by (5*3^n -1)/2 for n = 0, 1, 2, 3, ... . - Philippe Deléham, Feb 25 2012

EXAMPLE

First five rows:

1

2

3...4

4...10...8

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

MATHEMATICA

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

u[n_, 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[Factor[u[n, x]], {n, 1, z}]

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

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

TableForm[cu]

Flatten[%]    (* A207625 *)

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

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

TableForm[cv]

Flatten[%]    (* A207626 *)

CROSSREFS

Cf. A207628.

Sequence in context: A118263 A217478 A279788 * A102539 A240220 A250229

Adjacent sequences:  A207624 A207625 A207626 * A207628 A207629 A207630

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

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Last modified October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)