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A207624 Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section. 3
1, 2, 3, 3, 4, 8, 3, 5, 15, 14, 3, 6, 24, 37, 20, 3, 7, 35, 76, 71, 26, 3, 8, 48, 135, 184, 117, 32, 3, 9, 63, 218, 395, 372, 175, 38, 3, 10, 80, 329, 748, 951, 664, 245, 44, 3, 11, 99, 472, 1295, 2094, 1987, 1084, 327, 50, 3, 12, 120, 651, 2096, 4137, 5032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

FORMULA

u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.  u=A207624; v=A102662.

EXAMPLE

First five rows:

1

2

3...3

4...8....3

5...15...14...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*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[%]    (* A207624 *)

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

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

TableForm[cv]

Flatten[%]    (* A102662 *)

CROSSREFS

Cf. A102662.

Sequence in context: A140514 A240209 A047079 * A203990 A238812 A227269

Adjacent sequences:  A207621 A207622 A207623 * A207625 A207626 A207627

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 14 04:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)