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A207537 Triangle of coefficients of polynomials u(n,x) jointly generated with A207538; see Formula section. 4
1, 2, 1, 4, 3, 8, 8, 1, 16, 20, 5, 32, 48, 18, 1, 64, 112, 56, 7, 128, 256, 160, 32, 1, 256, 576, 432, 120, 9, 512, 1280, 1120, 400, 50, 1, 1024, 2816, 2816, 1232, 220, 11, 2048, 6144, 6912, 3584, 840, 72, 1, 4096, 13312, 16640, 9984, 2912, 364, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Another version in A201701. - Philippe Deléham, Mar 03 2012.

Subtriangle of the triangle given by (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 03 2012

Columns : A011782, A001792, A001793, A001794, A006974, A006975, A006976. - Philippe Deléham, Mar 03 2012

Diagonal sums : A052980. - Philippe Deléham, Mar 03 2012

LINKS

Table of n, a(n) for n=1..55.

FORMULA

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

where u(1,x)=1, v(1,x)=1.  Also, A207537=|A028297|.

T(n,k) = 2*T(n-1,k) + T(n-2,k-1). - Philippe Deléham, Mar 03 2012

G.f.: -(1+x*y)*x*y/(-1+2*x+x^2*y). - R. J. Mathar, Aug 11 2015

EXAMPLE

First seven rows:

1

2...1

4...3

8...8...1

16..20..5

32..48..18..1

64..112.56..7

Triangle A201701 begins :

1

1, 0

2, 1, 0

4, 3, 0, 0

8, 8, 1, 0, 0

16, 20, 5, 0, 0, 0

32, 48, 18, 1, 0, 0, 0

64, 112, 56, 7, 0, 0, 0, 0

... - Philippe Deléham, Mar 03 2012

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_] := u[n - 1, x] + v[n - 1, x]

Table[Factor[u[n, x]], {n, 1, z}]

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

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]  (* A207537, |A028297| *)

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

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

TableForm[cv]

Flatten[%]  (* A207538, |A133156| *)

CROSSREFS

Cf. A028297, A207538, A133156.

Sequence in context: A005291 A106624 A028297 * A114438 A238757 A262230

Adjacent sequences:  A207534 A207535 A207536 * A207538 A207539 A207540

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 18 2012

STATUS

approved

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Last modified October 19 07:56 EDT 2018. Contains 316337 sequences. (Running on oeis4.)