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Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.
7

%I #10 Feb 16 2019 18:15:09

%S 1,0,2,0,0,3,0,0,0,2,0,0,0,0,5,0,0,0,0,0,1,0,0,0,0,0,0,7,0,0,0,0,0,0,

%T 0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,0,0,

%U 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,13

%N Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.

%C A140579 * [1, 2, 3,...] = A140580.

%C (A140579)^(-1) * [1, 2, 3,...] = A048671: (1, 1, 1, 2, 1, 6, 1, 4, 3, 10,...).

%C A008683 = A140579^(-1) * A140664. - _Gary W. Adamson_, May 20 2008

%H G. C. Greubel, <a href="/A140579/b140579.txt">Rows n=1..100 of triangle, flattened</a>

%F Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.

%F Infinite lower triangular matrix with A014963 (1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11,...) in the main diagonal and the rest zeros.

%e First few rows of the triangle are:

%e 1;

%e 0, 2;

%e 0, 0, 3;

%e 0, 0, 0, 2;

%e 0, 0, 0, 0, 5;

%e 0, 0, 0, 0, 0, 1;

%e 0, 0, 0, 0, 0, 0, 7;

%e ...

%t Table[If[k != n ,0,Exp[MangoldtLambda[n]]], {n,1,12}, {k,1,n}]//Flatten (* _G. C. Greubel_, Feb 16 2019 *)

%o (PARI) {T(n,k) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*0^(n-k))};

%o for(n=1,12, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Feb 16 2019

%o (Sage)

%o def T(n,k): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*0^(n-k)

%o [[T(n,k) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Feb 16 2019

%Y Cf. A014963, A140580, A048671.

%Y Cf. A008683, A140664.

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_ and _Mats Granvik_, May 17 2008