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A174625 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.

%I A174625 #11 Aug 23 2013 12:52:40
%S A174625 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 A174625 77,44,11,2,36,105,112,54,12,13,91,182,156,65,13,2,49,196,294,210,77,
%U A174625 14,15,140,378,450,275,90,15,2,64,336,672,660,352,104,16,17,204,714,1122,935,442
%N A174625 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 A174625 The polynomials are defined by the recurrence starting with P_1(x)=0, P_2(x)=2.
%C A174625 The degree of the polynomial (row length minus 1) is A004526(n-2).
%C A174625 All coefficients of P_n are multiples of n iff n is prime.
%C A174625 Apparently a mirrored version of A157000. [R. J. Mathar, Nov 01 2010]
%e A174625 The table starts
%e A174625 0; # 0
%e A174625 2; # 2
%e A174625 3; # 3
%e A174625 2,4; # 4+2*x
%e A174625 5,5; # 5+5*x
%e A174625 2,9,6; # 6+9*x+2*x^2
%e A174625 7,14,7; # 7+14*x+7*x^2
%e A174625 2,16,20,8; # 8+20*x+16*x^2+2*x^3
%e A174625 9,30,27,9; # 9+27*x+30*x^2+9*x^3
%e A174625 2,25,50,35,10; # 10+35*x+50*x^2+25*x^3+2*x^4
%e A174625 11,55,77,44,11; # 11+44*x+77*x^2+55*x^3+11*x^4
%t A174625 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 A174625 Cf. A018187, A013998, A174531.
%K A174625 nonn,easy,tabf
%O A174625 1,2
%A A174625 _Vladimir Shevelev_, Mar 24 2010
%E A174625 Definition rephrased, sequence extended, keyword:tabf, examples added _R. J. Mathar_, Nov 01 2010