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A209157 Triangle of coefficients of polynomials v(n,x) jointly generated with A209154; see the Formula section. 3
1, 2, 2, 3, 6, 2, 4, 14, 12, 4, 5, 28, 40, 24, 4, 6, 50, 104, 96, 40, 8, 7, 82, 234, 304, 204, 72, 8, 8, 126, 476, 820, 768, 408, 112, 16, 9, 184, 896, 1968, 2408, 1760, 768, 192, 16, 10, 258, 1584, 4320, 6640, 6288, 3776, 1408, 288, 32, 11, 350, 2658 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last number of each row is a power of 2.

(n-th alternating row sum)=2-n for n>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)=2x*u(n-1,x)+v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

2...2

3...6....2

4...14...12...4

5...28...40...24...4

First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + x^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] + 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[%]    (* A209154 *)

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

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

TableForm[cv]

Flatten[%]    (* A209157 *)

CROSSREFS

Cf. A209154, A208510.

Sequence in context: A248164 A210222 A207621 * A284785 A076333 A015051

Adjacent sequences:  A209154 A209155 A209156 * A209158 A209159 A209160

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 20 20:18 EDT 2019. Contains 328273 sequences. (Running on oeis4.)