%I #14 Oct 29 2021 10:39:01
%S 1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,2,3,1,1,0,1,4,3,3,1,1,0,1,5,7,3,3,1,1,
%T 0,1,8,9,8,3,3,1,1,0,1,11,17,10,8,3,3,1,1,0,1,18,24,20,10,8,3,3,1,1,0,
%U 1,25,42,29,21,10,8,3,3,1,1,0,1,40,62,53,30,21,10,8,3,3,1,1,0,1
%N Triangle of the Multiset Transformation of A060280.
%H Alois P. Heinz, <a href="/A348422/b348422.txt">Rows n = 1..200, flattened</a>
%H <a href="/index/Mu#multiplicative_completely">Index entries for triangles generated by the Multiset Transformation</a>
%F G.f.: Product_{j>=1} 1/(1-y*x^j)^A060280(j). - _Jean-François Alcover_, Oct 29 2021
%e The triangle starts
%e 1
%e 0 1
%e 1 0 1
%e 1 1 0 1
%e 2 1 1 0 1
%e 2 3 1 1 0 1
%e 4 3 3 1 1 0 1
%e 5 7 3 3 1 1 0 1
%e 8 9 8 3 3 1 1 0 1
%e 11 17 10 8 3 3 1 1 0 1
%e 18 24 20 10 8 3 3 1 1 0 1
%e 25 42 29 21 10 8 3 3 1 1 0 1
%e 40 62 53 30 21 10 8 3 3 1 1 0 1
%e 58 105 80 56 30 21 10 8 3 3 1 1 0 1
%e 90 159 141 85 57 30 21 10 8 3 3 1 1 0 1
%e ...
%t nn = 13;
%t f[n_] := Fibonacci[n-1] + Fibonacci[n+1] - (-1)^n - 1;
%t b[n_] := (1/n) DivisorSum[n, MoebiusMu[#] f[n/#]&];
%t Rest@CoefficientList[#, y]& /@ (Series[Product[1/(1 - y x^i)^b[i], {i, 1, nn}], {x, 0, nn}] // Rest@CoefficientList[#, x]&) // Flatten (* _Jean-François Alcover_, Oct 29 2021 *)
%Y Cf. A060280 (column k=1), A000045 (row sums).
%K nonn,tabl
%O 1,11
%A _R. J. Mathar_, Oct 18 2021