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A209146 Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section. 4
1, 2, 1, 4, 5, 2, 7, 13, 11, 4, 12, 29, 34, 24, 8, 20, 60, 90, 85, 52, 16, 33, 118, 215, 255, 206, 112, 32, 54, 225, 481, 680, 683, 488, 240, 64, 88, 419, 1028, 1682, 1994, 1760, 1136, 512, 128, 143, 767, 2122, 3937, 5361, 5553, 4408, 2608, 1088, 256 (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,...

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

LINKS

Table of n, a(n) for n=1..55.

FORMULA

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

v(n,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

4...5...2

7...13...11...4

12...29...34...24...8

First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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_] := 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[%]    (* A209146 *)

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

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

TableForm[cv]

Flatten[%]    (* A209147 *)

CROSSREFS

Cf. A209146, A208510.

Sequence in context: A051176 A145064 A209166 * A209154 A144332 A209153

Adjacent sequences:  A209143 A209144 A209145 * A209147 A209148 A209149

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 06 2012

STATUS

approved

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Last modified October 14 07:19 EDT 2019. Contains 327995 sequences. (Running on oeis4.)