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 A208909 Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section. 3

%I #5 Mar 30 2012 18:58:14

%S 1,1,2,1,6,6,1,10,20,16,1,14,42,68,44,1,18,72,172,220,120,1,22,110,

%T 344,648,696,328,1,26,156,600,1480,2336,2160,896,1,30,210,956,2900,

%U 5984,8128,6608,2448,1,34,272,1428,5124,12984,23056,27536,19984

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; 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)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 1...2

%e 1...6...6

%e 1...10...20...16

%e 1...14...42...68...44

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

%e 1

%e 1 + 2x

%e 1 + 6x + 6x^2

%e 1 + 10x + 20x^2 + 16x^3

%e 1 + 14x + 42x^2 + 68x^3 + 44x^4

%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_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A208909 *)

%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[%] (* A208930 *)

%Y Cf. A208909, A208510.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Mar 04 2012

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Last modified September 13 11:52 EDT 2024. Contains 375905 sequences. (Running on oeis4.)