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A208908 Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section. 3
1, 2, 2, 2, 5, 4, 2, 9, 15, 8, 2, 13, 33, 37, 16, 2, 17, 59, 103, 91, 32, 2, 21, 93, 221, 297, 213, 64, 2, 25, 135, 407, 739, 807, 491, 128, 2, 29, 185, 677, 1553, 2285, 2105, 1109, 256, 2, 33, 243, 1047, 2907, 5391, 6675, 5319, 2475, 512, 2, 37, 309, 1533 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

2...5....4

2...9...15...8

2...13...33...37...16

First five polynomials v(n,x):

1

2 + 2x

2 + 5x + 4x^2

2 + 9x + 15x^2 + 8x^3

2 + 13x + 33x^2 + 37x^3 + 16x^4

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A208923 *)

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

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

TableForm[cv]

Flatten[%]    (* A208908 *)

CROSSREFS

Cf. A208923, A208510.

Sequence in context: A246119 A210562 A208512 * A209558 A209772 A147293

Adjacent sequences:  A208905 A208906 A208907 * A208909 A208910 A208911

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)