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A207618 Triangle of coefficients of polynomials u(n,x) jointly generated with A207619; see the Formula section. 3
1, 2, 3, 3, 4, 7, 6, 5, 12, 17, 12, 6, 18, 34, 40, 24, 7, 25, 58, 91, 92, 48, 8, 33, 90, 173, 234, 208, 96, 9, 42, 131, 295, 489, 584, 464, 192, 10, 52, 182, 467, 906, 1328, 1424, 1024, 384, 11, 63, 244, 700, 1545, 2651, 3496, 3408, 2240, 768, 12, 75, 318 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

3...3

4...7....6

5...12...17...12

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] + 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[%]    (* A207618 *)

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

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

TableForm[cv]

Flatten[%]    (* A207619 *)

CROSSREFS

Cf. A207619.

Sequence in context: A184271 A269098 A119795 * A119614 A260167 A035540

Adjacent sequences:  A207615 A207616 A207617 * A207619 A207620 A207621

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 18 05:45 EDT 2019. Contains 328146 sequences. (Running on oeis4.)