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A209152 Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; see the Formula section. 2
1, 2, 1, 3, 5, 3, 4, 10, 14, 7, 5, 16, 32, 37, 17, 6, 23, 58, 97, 98, 41, 7, 31, 93, 197, 287, 257, 99, 8, 40, 138, 348, 642, 830, 670, 239, 9, 50, 194, 562, 1234, 2024, 2360, 1737, 577, 10, 61, 262, 852, 2148, 4198, 6220, 6617, 4482, 1393, 11, 73, 343 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...5....3

4...10...14...7

5...16...32...37...17

First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 3x^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_] := x*u[n - 1, x] + 2 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[%]    (* A209152 *)

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

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

TableForm[cv]

Flatten[%]    (* A208339 *)

CROSSREFS

Cf. A208339, A208510.

Sequence in context: A322942 A060083 A069931 * A209158 A209135 A258236

Adjacent sequences:  A209149 A209150 A209151 * A209153 A209154 A209155

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)