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

1,2

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]

Links

Table of n, a(n) for n=1..71.

Example

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

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 *)

Crossrefs

Cf. A018187, A013998, A174531.

Sequence in context: A359369 A090321 A241255 * A178853 A344646 A120641

Adjacent sequences: A174622 A174623 A174624 * A174626 A174627 A174628

Keyword

nonn,easy,tabf

Author

Vladimir Shevelev, Mar 24 2010

Extensions

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

Status

approved