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A208526 Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section. 3
1, 1, 1, 1, 2, 4, 1, 3, 8, 10, 1, 4, 12, 22, 28, 1, 5, 16, 36, 68, 76, 1, 6, 20, 52, 120, 200, 208, 1, 7, 24, 70, 184, 376, 592, 568, 1, 8, 28, 90, 260, 608, 1184, 1736, 1552, 1, 9, 32, 112, 348, 900, 2016, 3672, 5072, 4240, 1, 10, 36, 136, 448, 1256, 3120 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

1...2...4

1...3...8....10

1...4...12...22...28

First five polynomials u(n,x):

1

1 + x

1 + 2x + 4x^2

1 + 3x + 8x^2 + 10x^3

1 + 4x + 12x^2 + 22x^3 + 28x^4

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A208526 *)

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

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

TableForm[cv]

Flatten[%]  (* A208527 *)

CROSSREFS

Cf. A208527.

Sequence in context: A290824 A272977 A230505 * A275895 A158613 A209573

Adjacent sequences:  A208523 A208524 A208525 * A208527 A208528 A208529

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 14 04:44 EDT 2019. Contains 327995 sequences. (Running on oeis4.)