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A208660 Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section. 3
1, 1, 2, 1, 8, 2, 1, 18, 14, 2, 1, 32, 52, 20, 2, 1, 50, 140, 104, 26, 2, 1, 72, 310, 380, 174, 32, 2, 1, 98, 602, 1106, 806, 262, 38, 2, 1, 128, 1064, 2744, 2924, 1472, 368, 44, 2, 1, 162, 1752, 6048, 8892, 6412, 2432, 492, 50, 2, 1, 200, 2730, 12168, 23652 (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..60.

FORMULA

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

v(n,x)=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....2

1...18...14...2

1...32...52...20...2

First five polynomials u(n,x):

1

1 + 2x

1 + 8x + 2x^2

1 + 18x + 14x^2 + 2x^3

1 + 32x + 52x^2 + 20x^3 + 2x^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_] := 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[%]    (* A208660 *)

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

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

TableForm[cv]

Flatten[%]    (* A208904 *)

CROSSREFS

Cf. A208904, A208510.

Sequence in context: A118961 A180956 A208921 * A114706 A046740 A317932

Adjacent sequences:  A208657 A208658 A208659 * A208661 A208662 A208663

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 19 20:58 EDT 2019. Contains 328224 sequences. (Running on oeis4.)