

A174625


Table T(n,k) with the coefficients of the polynomial P_n(x) = P_{n1}(x) + x*P_{n2}(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
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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(n2).
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[n1] +x p[n2]+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



