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A207626 Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section. 4
1, 2, 3, 3, 9, 3, 4, 20, 18, 3, 5, 38, 62, 27, 3, 6, 65, 164, 131, 36, 3, 7, 103, 369, 461, 227, 45, 3, 8, 154, 742, 1324, 1010, 350, 54, 3, 9, 220, 1372, 3298, 3578, 1892, 500, 63, 3, 10, 303, 2376, 7386, 10768, 8022, 3188, 677, 72, 3, 11, 405, 3903, 15222 (list; table; 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)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

2...3

3...9...3

4...20...18...3

5...38...62...27...3

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_] := 2 x*u[n - 1, x] + (x + 1)*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[%]    (* A207625 *)

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

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

TableForm[cv]

Flatten[%]    (* A207626 *)

CROSSREFS

Cf. A207625.

Sequence in context: A267563 A166994 A059083 * A232324 A124931 A210226

Adjacent sequences:  A207623 A207624 A207625 * A207627 A207628 A207629

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)