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A208754 Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section. 3
1, 3, 5, 2, 7, 10, 9, 28, 4, 11, 60, 28, 13, 110, 108, 8, 15, 182, 308, 72, 17, 280, 728, 352, 16, 19, 408, 1512, 1248, 176, 21, 570, 2856, 3600, 1040, 32, 23, 770, 5016, 8976, 4400, 416, 25, 1012, 8316, 20064, 14960, 2880, 64, 27, 1300, 13156, 41184 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3

5...2

7...10

9...28...4

First five polynomials v(n,x):

1

3

5 + 2x

7 + 10x

9 + 28x + 4x^2

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] + 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[%]    (* A208753 *)

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

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

TableForm[cv]

Flatten[%]    (* A208754 *)

CROSSREFS

Cf. A208753, A208510.

Sequence in context: A026184 A026208 A120837 * A180077 A095749 A137988

Adjacent sequences:  A208751 A208752 A208753 * A208755 A208756 A208757

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)