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A304963
Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1} x^(i*j*k)).
2
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.
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 22 2018
STATUS
approved