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A208923 Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section. 3
1, 1, 2, 1, 6, 4, 1, 10, 14, 8, 1, 14, 32, 38, 16, 1, 18, 58, 104, 90, 32, 1, 22, 92, 222, 296, 214, 64, 1, 26, 134, 408, 738, 808, 490, 128, 1, 30, 184, 678, 1552, 2286, 2104, 1110, 256, 1, 34, 242, 1048, 2906, 5392, 6674, 5320, 2474, 512, 1, 38, 308 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

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

1...2

1...6....4

1...10...14...8

1...14...32...38...16

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 4x^2

1 + 10x + 14x^2 + 8x^3

1 + 14x + 32x^2 + 38x^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. A208908, A208510.

Sequence in context: A133166 A293409 A051482 * A185045 A208913 A208911

Adjacent sequences:  A208920 A208921 A208922 * A208924 A208925 A208926

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)