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.

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, 77, 44, 11, 2, 36, 105, 112, 54, 12, 13, 91, 182, 156, 65, 13, 2, 49, 196, 294, 210, 77, 14, 15, 140, 378, 450, 275, 90, 15, 2, 64, 336, 672, 660, 352, 104, 16, 17, 204, 714, 1122, 935, 442

Offset: 1

Author

Vladimir Shevelev, Mar 24 2010

Keywords

• nonn
• easy
• tabf

Comments

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

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

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

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

Examples

			The table starts
0; # 0
2; # 2
3; # 3
2,4; # 4+2*x
5,5; # 5+5*x
2,9,6; # 6+9*x+2*x^2
7,14,7; # 7+14*x+7*x^2
2,16,20,8; # 8+20*x+16*x^2+2*x^3
9,30,27,9; # 9+27*x+30*x^2+9*x^3
2,25,50,35,10; # 10+35*x+50*x^2+25*x^3+2*x^4
11,55,77,44,11; # 11+44*x+77*x^2+55*x^3+11*x^4
		

Crossrefs

Cf. A018187, A013998, A174531.

Programs

Mathematica

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 *)

Extensions

Definition rephrased, sequence extended, keyword:tabf, examples added R. J. Mathar, Nov 01 2010