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A208922 Triangle of coefficients of polynomials v(n,x) jointly generated with A208921; see the Formula section. 3
1, 3, 1, 5, 4, 2, 7, 13, 12, 2, 9, 32, 40, 16, 4, 11, 65, 108, 80, 36, 4, 13, 116, 258, 288, 180, 48, 8, 15, 189, 560, 842, 700, 324, 96, 8, 17, 288, 1120, 2144, 2312, 1536, 640, 128, 16, 19, 417, 2088, 4944, 6728, 5832, 3232, 1088, 240, 16, 21, 580, 3666 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums:  1,2,3,4,5,6,7,8,9,10,...

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

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

EXAMPLE

First five rows:

1

3...1

5...4....2

7...13...12...2

9...32...40...16...4

First five polynomials v(n,x):

1

3 + x

5 + 4x + 2x^2

7 + 13x + 12x^2 + 2x^3

9 + 32x + 40x^2 + 16x^3 + 4x^4

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

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;

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. A208921, A208510.

Sequence in context: A131809 A016574 A210560 * A209770 A210799 A068512

Adjacent sequences:  A208919 A208920 A208921 * A208923 A208924 A208925

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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