A174625 - OEIS

%I #11 Aug 23 2013 12:52:40

%S 0,2,3,2,4,5,5,2,9,6,7,14,7,2,16,20,8,9,30,27,9,2,25,50,35,10,11,55,

%T 77,44,11,2,36,105,112,54,12,13,91,182,156,65,13,2,49,196,294,210,77,

%U 14,15,140,378,450,275,90,15,2,64,336,672,660,352,104,16,17,204,714,1122,935,442

%N Table T(n,k) with the coefficients of the polynomial P_n(x) = P_{n-1}(x) + x*P_{n-2}(x) + 1 in row n, by decreasing exponent of x.

%C The polynomials are defined by the recurrence starting with P_1(x)=0, P_2(x)=2.

%C The degree of the polynomial (row length minus 1) is A004526(n-2).

%C All coefficients of P_n are multiples of n iff n is prime.

%C Apparently a mirrored version of A157000. [R. J. Mathar, Nov 01 2010]

%e The table starts

%e 0; # 0

%e 2; # 2

%e 3; # 3

%e 2,4; # 4+2*x

%e 5,5; # 5+5*x

%e 2,9,6; # 6+9*x+2*x^2

%e 7,14,7; # 7+14*x+7*x^2

%e 2,16,20,8; # 8+20*x+16*x^2+2*x^3

%e 9,30,27,9; # 9+27*x+30*x^2+9*x^3

%e 2,25,50,35,10; # 10+35*x+50*x^2+25*x^3+2*x^4

%e 11,55,77,44,11; # 11+44*x+77*x^2+55*x^3+11*x^4

%t p[0]:=0 p[1]:=2; p[n_]:=p[n]=Expand[p[n-1] +x p[n-2]+1]; Flatten[{0, Map[Reverse[CoefficientList[#,x]]&, Table[Expand[p[n]], {n,0,20}]]}] (* _Peter J. C. Moses_, Aug 18 2013 *)

%Y Cf. A018187, A013998, A174531.

%K nonn,easy,tabf

%O 1,2

%A _Vladimir Shevelev_, Mar 24 2010

%E Definition rephrased, sequence extended, keyword:tabf, examples added _R. J. Mathar_, Nov 01 2010