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A207623 Triangle of coefficients of polynomials v(n,x) jointly generated with A207622; the see Formula section. 3
1, 2, 2, 3, 6, 4, 14, 4, 5, 28, 20, 6, 50, 64, 8, 7, 82, 164, 56, 8, 126, 364, 232, 16, 9, 184, 728, 736, 144, 10, 258, 1344, 1968, 736, 32, 11, 350, 2328, 4656, 2800, 352, 12, 462, 3828, 10032, 8800, 2144, 64, 13, 596, 6028, 20064, 24112, 9536, 832, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column n is divisible by 2^(n-1); row n ends with 2^(n-1).

Column 2: 2*A004006.

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

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

EXAMPLE

First five rows:

1

2...2

3...6

4...14...4

5...28...20

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] + 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[%]    (* A207622 *)

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

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

TableForm[cv]

Flatten[%]    (* A207623 *)

CROSSREFS

Cf. A207622.

Sequence in context: A185810 A015050 A284222 * A116447 A137757 A210751

Adjacent sequences:  A207620 A207621 A207622 * A207624 A207625 A207626

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)