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A207617 Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; the see Formula section. 3
1, 2, 1, 3, 3, 4, 7, 1, 5, 14, 5, 6, 25, 16, 1, 7, 41, 41, 7, 8, 63, 91, 29, 1, 9, 92, 182, 92, 9, 10, 129, 336, 246, 46, 1, 11, 175, 582, 582, 175, 11, 12, 231, 957, 1254, 550, 67, 1, 13, 298, 1507, 2508, 1507, 298, 13, 14, 377, 2288, 4719, 3718, 1079, 92, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

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

EXAMPLE

First five rows:

1

2...1

3...3

4...7...1

5...14...5

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*u[n - 1, 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[%]    (* A207616  *)

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

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

TableForm[cv]

Flatten[%]    (* A207617 *)

CROSSREFS

Cf. A207616.

Sequence in context: A032215 A117363 A007307 * A141576 A078019 A038071

Adjacent sequences:  A207614 A207615 A207616 * A207618 A207619 A207620

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)