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A208931 Triangle of coefficients of polynomials u(n,x) jointly generated with A208932; see the Formula section. 3
1, 1, 2, 1, 8, 4, 1, 18, 20, 8, 1, 32, 64, 56, 16, 1, 50, 160, 224, 136, 32, 1, 72, 340, 680, 664, 328, 64, 1, 98, 644, 1736, 2416, 1872, 760, 128, 1, 128, 1120, 3920, 7264, 7856, 4984, 1736, 256, 1, 162, 1824, 8064, 19056, 26992, 23768, 12832, 3896 (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..54.

FORMULA

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

EXAMPLE

First five rows:

1

1...2

1...8....4

1...18...20...8

1...32...64...56...16

First five polynomials u(n,x):

1

1 + 2x

1 + 8x + 4x^2

1 + 18x + 20x^2 + 8x^3

1 + 32x + 64x^2 + 56x^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 + 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[%]    (* A208931 *)

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

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

TableForm[cv]

Flatten[%]    (* A208932 *)

CROSSREFS

Cf. A208931, A208510.

Sequence in context: A200584 A099379 A234014 * A133214 A191935 A142075

Adjacent sequences:  A208928 A208929 A208930 * A208932 A208933 A208934

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)