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A208754 Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section. 3

%I #6 Mar 30 2012 18:58:14

%S 1,3,5,2,7,10,9,28,4,11,60,28,13,110,108,8,15,182,308,72,17,280,728,

%T 352,16,19,408,1512,1248,176,21,570,2856,3600,1040,32,23,770,5016,

%U 8976,4400,416,25,1012,8316,20064,14960,2880,64,27,1300,13156,41184

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section.

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

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

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

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

%e First five rows:

%e 1

%e 3

%e 5...2

%e 7...10

%e 9...28...4

%e First five polynomials v(n,x):

%e 1

%e 3

%e 5 + 2x

%e 7 + 10x

%e 9 + 28x + 4x^2

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

%t u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

%t v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

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

%t TableForm[cu]

%t Flatten[%] (* A208753 *)

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

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

%t TableForm[cv]

%t Flatten[%] (* A208754 *)

%Y Cf. A208753, A208510.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Mar 03 2012

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)