This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348422 #14 Oct 29 2021 10:39:01 %S A348422 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 A348422 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 A348422 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 A348422 Triangle of the Multiset Transformation of A060280. %H A348422 Alois P. Heinz, <a href="/A348422/b348422.txt">Rows n = 1..200, flattened</a> %H A348422 <a href="/index/Mu#multiplicative_completely">Index entries for triangles generated by the Multiset Transformation</a> %F A348422 G.f.: Product_{j>=1} 1/(1-y*x^j)^A060280(j). - _Jean-François Alcover_, Oct 29 2021 %e A348422 The triangle starts %e A348422 1 %e A348422 0 1 %e A348422 1 0 1 %e A348422 1 1 0 1 %e A348422 2 1 1 0 1 %e A348422 2 3 1 1 0 1 %e A348422 4 3 3 1 1 0 1 %e A348422 5 7 3 3 1 1 0 1 %e A348422 8 9 8 3 3 1 1 0 1 %e A348422 11 17 10 8 3 3 1 1 0 1 %e A348422 18 24 20 10 8 3 3 1 1 0 1 %e A348422 25 42 29 21 10 8 3 3 1 1 0 1 %e A348422 40 62 53 30 21 10 8 3 3 1 1 0 1 %e A348422 58 105 80 56 30 21 10 8 3 3 1 1 0 1 %e A348422 90 159 141 85 57 30 21 10 8 3 3 1 1 0 1 %e A348422 ... %t A348422 nn = 13; %t A348422 f[n_] := Fibonacci[n-1] + Fibonacci[n+1] - (-1)^n - 1; %t A348422 b[n_] := (1/n) DivisorSum[n, MoebiusMu[#] f[n/#]&]; %t A348422 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 A348422 Cf. A060280 (column k=1), A000045 (row sums). %K A348422 nonn,tabl %O A348422 1,11 %A A348422 _R. J. Mathar_, Oct 18 2021