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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A119465 A090321 A241255 * A178853 A120641 A008666

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

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Last modified October 31 05:06 EDT 2020. Contains 338098 sequences. (Running on oeis4.)