A308153 G.f.: x * Product_{j>=1, k>=1} 1/(1 - a(j)*x^(j*k)).

1, 1, 3, 7, 19, 47, 134, 357, 1031, 2912, 8612, 25007, 75378, 223884, 683915, 2067578, 6376800, 19503546, 60749341, 187592661, 587938043, 1831377952, 5773159368, 18092820941, 57328904204, 180657986051, 574735018826, 1820143698295, 5810522774503, 18473074695503

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Maple

A:= proc(n) option remember; series(x*`if`(n=1, 1, mul(mul(
      1/(1-a(j)*x^(j*k)), k=1..(n-1)/j), j=1..n-1)), x, n+1)
    end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=1..35);  # Alois P. Heinz, May 14 2019

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[Product[1/(1 - a[j] x^(j k)), {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 30}]

Crossrefs

Cf. A093637, A179467, A308154.

Sequence in context: A181360 A001372 A179467 * A049117 A146810 A246493

Adjacent sequences: A308150 A308151 A308152 * A308154 A308155 A308156

Keyword

nonn

Author

Ilya Gutkovskiy, May 14 2019

Status

approved