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Triangle read by rows: row 0 is 1; for n>0, row n gives 1^n, prime(1)^n, prime(2)^n, ..., prime(n)^n.
4

%I #11 Sep 26 2014 12:49:31

%S 1,1,2,1,4,9,1,8,27,125,1,16,81,625,2401,1,32,243,3125,16807,161051,1,

%T 64,729,15625,117649,1771561,4826809,1,128,2187,78125,823543,19487171,

%U 62748517,410338673,1,256,6561,390625,5764801,214358881,815730721

%N Triangle read by rows: row 0 is 1; for n>0, row n gives 1^n, prime(1)^n, prime(2)^n, ..., prime(n)^n.

%C Polynomials like x^2+2^2*x+3^2 and x^4+2^4+x^3+3^4*x^2+5^4*x+7^4 inspired this sequence.

%e 1

%e 1, 2

%e 1, 4, 9

%e 1, 8, 27, 125

%e 1, 16, 81, 625, 2401

%e 1, 32, 243, 3125, 16807, 161051

%t T[n_, m_] := If[n == 0, 1,Prime[n]^m] a = Table[Table[T[n, m], {n, 0, m}], {m, 0, 10}] b = Flatten[a] MatrixForm[a]

%t Module[{nn=10,pr},pr=Prime[Range[nn]];Flatten[Table[Join[{1},Take[pr, n]^n],{n,0,nn}]]] (* _Harvey P. Dale_, Sep 26 2014 *)

%Y Rows n=1, 2, 3, .., 7 are A000040, A001248, A030078, A030514, A050997, A030516 and A092759. - _R. J. Mathar_, Mar 23 2007

%K nonn,tabl

%O 0,3

%A _Roger L. Bagula_, Jun 24 2006

%E Edited by _N. J. A. Sloane_, Mar 26 2007