A348422 Triangle of the Multiset Transformation of A060280.

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, 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, 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

Offset: 1

Author

R. J. Mathar, Oct 18 2021

Keywords

• nonn
• tabl

Examples

			The triangle starts
   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   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   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
  58 105  80  56  30  21  10   8   3   3   1   1   0   1
  90 159 141  85  57  30  21  10   8   3   3   1   1   0   1
  ...
		

Links

• Alois P. Heinz, Rows n = 1..200, flattened
• Index entries for triangles generated by the Multiset Transformation

Crossrefs

Cf. A060280 (column k=1), A000045 (row sums).

Programs

Mathematica

nn = 13;
f[n_] := Fibonacci[n-1] + Fibonacci[n+1] - (-1)^n - 1;
b[n_] := (1/n) DivisorSum[n, MoebiusMu[#] f[n/#]&];
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 *)

Formula

G.f.: Product_{j>=1} 1/(1-y*x^j)^A060280(j). - Jean-François Alcover, Oct 29 2021