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A210559 Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section. 4
1, 1, 2, 1, 4, 3, 1, 6, 8, 5, 1, 8, 15, 17, 8, 1, 10, 24, 38, 33, 13, 1, 12, 35, 70, 86, 63, 21, 1, 14, 48, 115, 180, 187, 117, 34, 1, 16, 63, 175, 330, 437, 390, 214, 55, 1, 18, 80, 252, 553, 882, 1007, 791, 386, 89, 1, 20, 99, 348, 868, 1610, 2219, 2235, 1567 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

1...4...3

1...6...8....5

1...8...15...17...8

First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, 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[%]  (* A210559 *)

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

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

TableForm[cv]

Flatten[%]  (* A210560 *)

CROSSREFS

Cf. A210560, A208510.

Sequence in context: A197871 A093010 A179000 * A180803 A093966 A103406

Adjacent sequences:  A210556 A210557 A210558 * A210560 A210561 A210562

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 22 2012

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)