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A208930 Triangle of coefficients of polynomials v(n,x) jointly generated with A208930; see the Formula section. 4
1, 2, 3, 2, 7, 8, 2, 11, 26, 22, 2, 15, 52, 88, 60, 2, 19, 86, 214, 288, 164, 2, 23, 128, 416, 820, 916, 448, 2, 27, 178, 710, 1824, 2984, 2856, 1224, 2, 31, 236, 1112, 3500, 7464, 10464, 8768, 3344, 2, 35, 302, 1638, 6080, 15884, 29040, 35664, 26592 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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

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

EXAMPLE

First five rows:

1

2...3

2...7....8

2...11...26...22

2...15...52...88...60

First five polynomials v(n,x):

1

2 + 3x

2 + 7x + 8x^2

2 + 11x + 26x^2 + 22x^3

2 + 15x + 52x^2 + 88x^3 + 60x^4

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]    (* A208909 *)

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

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

TableForm[cv]

Flatten[%]    (* A208930 *)

CROSSREFS

Cf. A208909, A208510.

Sequence in context: A122697 A129022 A210564 * A122076 A209774 A271322

Adjacent sequences:  A208927 A208928 A208929 * A208931 A208932 A208933

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified December 5 05:13 EST 2021. Contains 349530 sequences. (Running on oeis4.)