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A207620 Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section. 3
1, 2, 4, 2, 7, 8, 2, 11, 21, 12, 2, 16, 45, 43, 16, 2, 22, 85, 119, 73, 20, 2, 29, 147, 280, 249, 111, 24, 2, 37, 238, 588, 705, 451, 157, 28, 2, 46, 366, 1134, 1749, 1496, 741, 211, 32, 2, 56, 540, 2046, 3927, 4290, 2821, 1135, 273, 36, 2, 67, 770, 3498 (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)+(x+1)*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

2

4...2

7...8...2

11...21...12...2

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] + (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[%]    (* A207620 *)

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

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

TableForm[cv]

Flatten[%]    (* A207621 *)

CROSSREFS

Cf. A207621.

Sequence in context: A214789 A207631 A207612 * A207622 A073017 A296092

Adjacent sequences:  A207617 A207618 A207619 * A207621 A207622 A207623

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)