A304964 Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)).

1, 1, 5, 13, 47, 133, 443, 1333, 4263, 13143, 41419, 128791, 403815, 1259639, 3941579, 12310299, 38492034, 120271953, 375964616, 1174935195, 3672413322, 11477465221, 35872928244, 112117013835, 350417746650, 1095202995267, 3422999582632, 10698350241417, 33437065631262, 104505382585023

Offset: 0

Author

Ilya Gutkovskiy, May 22 2018

Keywords

• nonn

Comments

Invert transform of A007426.

Links

• N. J. A. Sloane, Transforms
• Index entries for sequences related to compositions

Crossrefs

Cf. A000005, A007426, A011782, A129921, A280486, A280487, A304963.

Programs

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, 4)*a(n-j), j=1..n))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, May 22 2018

Mathematica

nmax = 29; CoefficientList[Series[1/(1 - Sum[x^(i j k l), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}, {l, 1, nmax/i/j/k}]), {x, 0, nmax}], x]
nmax = 29; CoefficientList[Series[1/(1 - Sum[Sum[DivisorSigma[0, d] DivisorSigma[0, k/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] DivisorSigma[0, k/d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}]

Formula

G.f.: 1/(1 - Sum_{k>=1} A007426(k)*x^k).