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A208750 Triangle of coefficients of polynomials v(n,x) jointly generated with A208749; see the Formula section. 3
1, 2, 1, 3, 4, 2, 4, 11, 10, 2, 5, 24, 32, 16, 4, 6, 45, 84, 72, 32, 4, 7, 76, 194, 240, 156, 48, 8, 8, 119, 406, 666, 592, 300, 88, 8, 9, 176, 784, 1632, 1896, 1344, 576, 128, 16, 10, 249, 1416, 3648, 5344, 4904, 2848, 1024, 224, 16, 11, 340, 2418, 7584 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Subtriangle of the triangle T(n,k) given by (1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 16 2012

LINKS

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

FORMULA

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

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

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

As DELTA-triangle with 0<=k<=n : G.f.: (1-x+x^2-y*x^2-2*t^2*x^2)/(1-2*x+x^2-2*y*x^2-2*y^2*x^2). - Philippe Deléham, Mar 16 2012

As DELTA-triangle : T(n,k) = 2*T(n-1,k) - T(n-2,k) + 2*T(n-2,k-1) + 2*T(n-2,k-2), T(0,0) = T(1,0) = T(2,1) = 1, T(2,0) = 2, T(1,1) = T(2,2) = 0 and T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 16 2012

EXAMPLE

First five rows:

1

2...1

3...4....2

4...11...10...2

5...24...32...16...4

First five polynomials v(n,x):

1

2 + x

3 + 4x + 2x^2

4 + 11x + 10x^2 + 2x^3

5 + 24x + 32x^2 + 16x^3 + 4x^4

(1, 1, -1, 1, 0, 0, ...) DELTA (0, 1, 1, -2, 0, 0, ...) begins :

1

1, 0

2, 1, 0

3, 4, 2, 0

4, 11, 10, 2, 0

5, 24, 32, 16, 4, 0

6, 45, 84, 72, 32, 4, 0 . Philippe Deléham, Mar 16 2012

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] + v[n - 1, x];

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[%]    (* A208749 *)

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

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

TableForm[cv]

Flatten[%]    (* A208750 *)

CROSSREFS

Cf. A208749, A208510.

Sequence in context: A102756 A086614 A108959 * A107893 A131987 A120874

Adjacent sequences:  A208747 A208748 A208749 * A208751 A208752 A208753

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 02 2012

STATUS

approved

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Last modified April 21 20:41 EDT 2019. Contains 322328 sequences. (Running on oeis4.)