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A207635 Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section. 3
1, 2, 5, 2, 11, 9, 2, 23, 29, 13, 2, 47, 81, 55, 17, 2, 95, 209, 191, 89, 21, 2, 191, 513, 591, 369, 131, 25, 2, 383, 1217, 1695, 1329, 631, 181, 29, 2, 767, 2817, 4607, 4353, 2591, 993, 239, 33, 2, 1535, 6401, 12031, 13313, 9535, 4577, 1471, 305, 37, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

v(n,x)=(x+1)*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

5....2

11...9....2

23...29...13...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 + 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[%]  (* A207635 *)

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

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

TableForm[cv]

Flatten[%]  (* A207636 *)

CROSSREFS

Cf. A207636.

Sequence in context: A276609 A292591 A240760 * A205715 A181338 A211175

Adjacent sequences:  A207632 A207633 A207634 * A207636 A207637 A207638

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 24 2012

STATUS

approved

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Last modified October 14 03:58 EDT 2019. Contains 327995 sequences. (Running on oeis4.)