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A210859 Triangle of coefficients of polynomials v(n,x) jointly generated with A210858; see the Formula section. 3
1, 2, 2, 3, 6, 3, 4, 16, 17, 5, 5, 35, 62, 40, 8, 6, 66, 189, 206, 90, 13, 7, 112, 494, 822, 603, 191, 21, 8, 176, 1133, 2787, 3101, 1638, 393, 34, 9, 261, 2337, 8255, 13209, 10483, 4175, 786, 55, 10, 370, 4427, 21730, 48753, 55089, 32705, 10157, 1540 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with 1 and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Alternating row sums:  1,0,0,0,0,0,0,0,...

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

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

3...6....3

4...16...17...5

5...35...62...40...8

First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + 3x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

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

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

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[%]   (* A210858 *)

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

TableForm[cv]

Flatten[%]   (* A210859 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]

Table[v[n, x] /. x -> 1, {n, 1, z}]

Table[u[n, x] /. x -> -1, {n, 1, z}]

Table[v[n, x] /. x -> -1, {n, 1, z}]

CROSSREFS

Cf. A210858, A208510.

Sequence in context: A208340 A308503 A196967 * A209420 A317449 A222310

Adjacent sequences:  A210856 A210857 A210858 * A210860 A210861 A210862

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 20 16:05 EDT 2019. Contains 328268 sequences. (Running on oeis4.)