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A207631 Triangle of coefficients of polynomials u(n,x) jointly generated with A207632; see the Formula section. 3
1, 2, 4, 2, 7, 6, 2, 12, 15, 8, 2, 20, 33, 25, 10, 2, 33, 68, 66, 37, 12, 2, 54, 134, 159, 113, 51, 14, 2, 88, 256, 359, 309, 176, 67, 16, 2, 143, 478, 774, 781, 536, 257, 85, 18, 2, 232, 877, 1611, 1864, 1493, 860, 358, 105, 20, 2, 376, 1587, 3262, 4256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..60.

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

4...2

7...6...2

12...15...8...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 + 1)*u[n - 1, x] + 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[%]  (* A207631 *)

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

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

TableForm[cv]

Flatten[%]  (* A207632 *)

CROSSREFS

Cf. A207632.

Sequence in context: A228367 A110925 A214789 * A207612 A207620 A207622

Adjacent sequences:  A207628 A207629 A207630 * A207632 A207633 A207634

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 23 2012

STATUS

approved

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Last modified October 22 10:24 EDT 2019. Contains 328317 sequences. (Running on oeis4.)