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A209161 Triangle of coefficients of polynomials v(n,x) jointly generated with A209160; see the Formula section. 3
1, 1, 4, 1, 6, 10, 1, 8, 24, 28, 1, 10, 42, 88, 76, 1, 12, 64, 188, 300, 208, 1, 14, 90, 336, 760, 984, 568, 1, 16, 120, 540, 1560, 2880, 3136, 1552, 1, 18, 154, 808, 2820, 6672, 10416, 9792, 4240, 1, 20, 192, 1148, 4676, 13392, 26880, 36384, 30096 (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..54.

FORMULA

u(n,x)=u(n-1,x)+(x+1)*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...4

1...6...10

1...8...24...28

1...10...42...88...76

First three polynomials v(n,x): 1, 1 + 4x, 1 + 6x + 10x^2.

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + (x + 1)*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[%]    (* A209160 *)

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

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

TableForm[cv]

Flatten[%]    (* A209161 *)

CROSSREFS

Cf. A209160, A208510.

Sequence in context: A124739 A122662 A210228 * A083843 A094264 A298829

Adjacent sequences:  A209158 A209159 A209160 * A209162 A209163 A209164

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 18 00:03 EDT 2019. Contains 328135 sequences. (Running on oeis4.)