A304963 Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1} x^(i*j*k)).

1, 1, 4, 10, 31, 82, 241, 664, 1898, 5316, 15058, 42374, 119718, 337432, 952373, 2685906, 7578248, 21376331, 60306495, 170120330, 479922212, 1353855927, 3819280961, 10774233218, 30394408336, 85743168417, 241883489742, 682358211402, 1924947591447, 5430317571250, 15319043353639

Offset

0,3

Comments

Invert transform of A007425.

Links

Table of n, a(n) for n=0..30.

N. J. A. Sloane, Transforms

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} A007425(k)*x^k).

Maple

A:= proc(n, k) option remember; `if`(k=1, 1,
      add(A(d, k-1), d=numtheory[divisors](n)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(A(j, 3)*a(n-j), j=1..n))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, May 22 2018

Mathematica

nmax = 30; CoefficientList[Series[1/(1 - Sum[x^(i j k), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}]), {x, 0, nmax}], x]
nmax = 30; CoefficientList[Series[1/(1 - Sum[Sum[DivisorSigma[0, d], {d, Divisors[k]}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[DivisorSigma[0, d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]

Crossrefs

Cf. A000005, A007425, A011782, A129921, A174465, A280473, A304964.

Sequence in context: A346754 A333916 A264564 * A034730 A321143 A095127

Adjacent sequences: A304960 A304961 A304962 * A304964 A304965 A304966

Keyword

nonn

Author

Ilya Gutkovskiy, May 22 2018

Status

approved