A208932 - OEIS

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

%S 1,3,2,5,8,4,7,22,24,8,9,48,84,60,16,11,90,228,264,148,32,13,152,528,

%T 876,772,348,64,15,238,1092,2424,2992,2112,804,128,17,352,2072,5896,

%U 9568,9392,5548,1820,256,19,498,3672,13008,26648,34080,27780

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A208932; see the Formula section.

%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

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

%e First five rows:

%e 1

%e 3...2

%e 5...8....4

%e 7...22...24...8

%e 9...48...84...60...16

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

%e 1

%e 3 + 2x

%e 5 + 8x + 4x^2

%e 7 + 22x + 24x^2 + 8x^3

%e 9 + 48x + 84x^2 + 60x^3 + 16x^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] + (x + 1)*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[%]    (* A208931 *)

%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[%]    (* A208932 *)

%Y Cf. A208930, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 04 2012