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A207634 Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section. 3
1, 2, 3, 3, 6, 6, 5, 13, 15, 12, 8, 26, 41, 36, 24, 13, 50, 95, 115, 84, 48, 21, 94, 210, 300, 302, 192, 96, 34, 173, 443, 740, 871, 760, 432, 192, 55, 314, 905, 1716, 2353, 2392, 1856, 960, 384, 89, 563, 1803, 3823, 5916, 6987, 6312, 4432, 2112, 768 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: Fibonacci numbers, A000045.

LINKS

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

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...3

3...6....6

5...13...15...12

8...26...41...36...24

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1

Table[Factor[u[n, x]], {n, 1, z}]

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

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A207633 *)

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

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

TableForm[cv]

Flatten[%]  (* A207634 *)

CROSSREFS

Cf. A207633.

Sequence in context: A321745 A212629 A127779 * A222862 A101437 A039856

Adjacent sequences:  A207631 A207632 A207633 * A207635 A207636 A207637

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 24 2012

STATUS

approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)