A209150 - OEIS

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A209150

Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.

1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 11, 21, 17, 7, 1, 16, 40, 46, 28, 8, 1, 22, 71, 107, 87, 39, 10, 1, 29, 119, 224, 232, 144, 55, 11, 1, 37, 190, 434, 555, 443, 226, 70, 13, 1, 46, 291, 792, 1221, 1198, 773, 328, 91, 14, 1, 56, 430, 1377, 2511, 2942, 2318, 1255

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OFFSET

1,2

COMMENTS

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

EXAMPLE

First five rows:

2...1

4...4.....1

7...10....5....1

11...21...17...7...1

First three polynomials v(n,x): 1, 2 + x, 4 + 4x + x^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_] := 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[%] (* A209150 *)

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

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

TableForm[cv]

Flatten[%] (* A208335 *)

CROSSREFS

Cf. A208335, A208510.

Sequence in context: A154558 A220836 A008572 * A209145 A333650 A214984

Adjacent sequences: A209147 A209148 A209149 * A209151 A209152 A209153

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved