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A208762 Triangle of coefficients of polynomials v(n,x) jointly generated with A208761; see the Formula section. 3
1, 2, 2, 3, 7, 4, 4, 17, 21, 8, 5, 34, 68, 55, 16, 6, 60, 174, 225, 137, 32, 7, 97, 384, 705, 674, 327, 64, 8, 147, 763, 1863, 2489, 1883, 761, 128, 9, 212, 1400, 4362, 7640, 8012, 5016, 1735, 256, 10, 294, 2412, 9318, 20542, 27996, 24144, 12885, 3897 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,0,0,0,0,0,0,0,0,...  For a discussion and guide to related arrays, see A208510.

As triangle T(n,k) with 0<=k<=n, it is (2, -1/2, 1/2, 0 0 0 0 0 0 0 ...) DELTA (2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 04 2012

Row sums are in A055099. - Philippe Deléham, Mar 04 2012

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

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

As triangle T(n,k) with 0<=k<=n : T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) + T(n-2,k-1) + 2*T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k>n or if k<0. - Philippe Deléham, Mar 04 2012

G.f.: (-1-x*y)*x*y/(-1+x*y+x^2*y+2*x^2*y^2+2*x-x^2). - R. J. Mathar, Aug 12 2015

EXAMPLE

First five rows:

1

2...2

3...7....4

4...17...21...8

5...34...68...55...16

First five polynomials v(n,x):

1

2 + 2x

3 + 7x + 4x^2

4 + 17x + 22x^2 + 8x^3

5 + 34x + 68x^2 + 55x^3 + 16x^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] + (x + 1) 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[%]    (* A208761 *)

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

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

TableForm[cv]

Flatten[%]    (* A208762 *)

CROSSREFS

Cf. A208761, A208510.

Sequence in context: A222779 A222894 A210753 * A209746 A267822 A210598

Adjacent sequences:  A208759 A208760 A208761 * A208763 A208764 A208765

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)