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

1,11

Links

Alois P. Heinz, Rows n = 1..200, flattened

Index entries for triangles generated by the Multiset Transformation

Formula

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

Example

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
  ...

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 *)

Crossrefs

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

Sequence in context: A247418 A229899 A153764 * A294509 A059571 A027052

Adjacent sequences: A348419 A348420 A348421 * A348423 A348424 A348425

Keyword

nonn,tabl

Author

R. J. Mathar, Oct 18 2021

Status

approved