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A208921 Triangle of coefficients of polynomials u(n,x) jointly generated with A208922; see the Formula section. 3
1, 1, 2, 1, 8, 2, 1, 18, 10, 4, 1, 32, 36, 28, 4, 1, 50, 100, 108, 36, 8, 1, 72, 230, 324, 196, 80, 8, 1, 98, 462, 840, 772, 440, 104, 16, 1, 128, 840, 1960, 2456, 1840, 752, 208, 16, 1, 162, 1416, 4200, 6744, 6464, 3824, 1488, 272, 32, 1, 200, 2250, 8376 (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..59.

FORMULA

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

v(n,x)=(x+1)*u(n-1,x)+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...10...4

1...32...36...28...4

First five polynomials u(n,x):

1

1 + 2x

1 + 8x + 2x^2

1 + 18x + 10x^2 + 4x^3

1 + 32x + 36x^2 + 28x^3 + 4x^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] + 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[%]    (* A208921 *)

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

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

TableForm[cv]

Flatten[%]    (* A208922 *)

CROSSREFS

Cf. A208922, A208510.

Sequence in context: A020778 A118961 A180956 * A208660 A114706 A046740

Adjacent sequences:  A208918 A208919 A208920 * A208922 A208923 A208924

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)