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A209163 Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section. 3
1, 2, 3, 3, 9, 5, 4, 20, 26, 11, 5, 38, 82, 71, 21, 6, 65, 204, 279, 176, 43, 7, 103, 439, 849, 845, 425, 85, 8, 154, 854, 2192, 3050, 2386, 990, 171, 9, 220, 1540, 5034, 9174, 9940, 6396, 2267, 341, 10, 303, 2616, 10578, 24232, 34102, 30228, 16521 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,-1,-1,-1,-,1-,1-,1,-1,...

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

v(n,x)=2x*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

2...3

3...9...5

4...20...26...11

5...38...82...71...21

First three polynomials v(n,x): 1, 2 + 3x, 3 + 9x + 5x^2.

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := 2 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[%]    (* A209162 *)

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

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

TableForm[cv]

Flatten[%]    (* A209163 *)

CROSSREFS

Cf. A209162, A208510.

Sequence in context: A232324 A124931 A210226 * A124932 A248788 A194232

Adjacent sequences:  A209160 A209161 A209162 * A209164 A209165 A209166

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)