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A209159 Triangle of coefficients of polynomials v(n,x) jointly generated with A209158; see the Formula section. 3
1, 1, 3, 1, 5, 5, 1, 7, 15, 11, 1, 9, 29, 41, 21, 1, 11, 47, 99, 103, 43, 1, 13, 69, 193, 301, 249, 85, 1, 15, 95, 331, 687, 851, 583, 171, 1, 17, 125, 521, 1349, 2225, 2285, 1337, 341, 1, 19, 159, 771, 2391, 4923, 6735, 5907, 3015, 683, 1, 21, 197, 1089 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternating row sums: 1,-2,1,-2,1,-2,1,-2,1,-2,...

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

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...3

1...5...5

1...7...15...11

1...9...29...41...21

First three polynomials v(n,x): 1, 1 + 3x, 1 + 5x + 5x^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] + 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[%]    (* A209158 *)

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

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

TableForm[cv]

Flatten[%]    (* A209159 *)

CROSSREFS

Cf. A209158, A208510.

Sequence in context: A084533 A082985 A111125 * A182397 A209560 A211977

Adjacent sequences:  A209156 A209157 A209158 * A209160 A209161 A209162

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)