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A209748 Triangle of coefficients of polynomials v(n,x) jointly generated with A209747; see the Formula section. 3
1, 3, 5, 2, 9, 6, 2, 15, 16, 8, 2, 25, 36, 26, 10, 2, 41, 76, 70, 38, 12, 2, 67, 152, 172, 118, 52, 14, 2, 109, 294, 394, 328, 182, 68, 16, 2, 177, 554, 860, 840, 562, 264, 86, 18, 2, 287, 1024, 1808, 2028, 1584, 894, 366, 106, 20, 2, 465, 1864, 3692, 4676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,3,3,5,5,7,7,9,9,...

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3

5....2

9....6....2

15...16...8...2

First three polynomials v(n,x): 1, 3, 5 + 2x.

MATHEMATICA

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

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

v[n_, x_] := 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[%]    (* A209747 *)

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

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

TableForm[cv]

Flatten[%]    (* A209748 *)

CROSSREFS

Cf. A209647, A208510.

Sequence in context: A275846 A273668 A245653 * A065172 A026188 A026212

Adjacent sequences:  A209745 A209746 A209747 * A209749 A209750 A209751

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 13 2012

STATUS

approved

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Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)