A308154 G.f.: x * Product_{j>=1, k>=1} (1 + a(j)*x^(j*k)).

1, 1, 2, 5, 11, 26, 64, 159, 397, 1042, 2701, 7249, 19341, 52927, 143615, 399359, 1099846, 3087498, 8616361, 24386458, 68617936, 195678409, 554862501, 1590363317, 4539073167, 13071768304, 37496646028, 108449257539, 312439316258, 906653694239, 2622887257356

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Maple

A:= proc(n) option remember; series(x*`if`(n=1, 1, mul(mul(
      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 + a[j] x^(j k)), {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 32}]

Crossrefs

Cf. A032305, A308060, A308153.

Sequence in context: A051286 A192475 A192400 * A182053 A306563 A308060

Adjacent sequences: A308151 A308152 A308153 * A308155 A308156 A308157

Keyword

nonn

Author

Ilya Gutkovskiy, May 14 2019

Status

approved