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Triangle of the Multiset Transformation of A060280.
2

%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