OFFSET
0,4
COMMENTS
Weigh transform of A051064.
FORMULA
G.f.: Product_{k>=1} (1 + x^k)^A051064(k).
Let A(x) be the g.f. of this sequence, and B(x) be the g.f. of A000009, then B(x) = A(x)/A(x^3). - Seiichi Manyama, May 31 2024
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^k)^IntegerExponent[3 k, 3], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d IntegerExponent[3 d, 3], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 50}]
PROG
(PARI) seq(n)={Vec(prod(k=1, n, (1 + x^k + O(x*x^n))^(1+valuation(k, 3))))} \\ Andrew Howroyd, Sep 23 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 23 2019
STATUS
approved