OFFSET
0,2
COMMENTS
Convolution inverse of A147655.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3321
FORMULA
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*prime(j)^k*x^(j*k)/k).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, b(n-i, i-1)*ithprime(i))))
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i$2)*a(i$2), i=0..n-1))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jun 13 2018
MATHEMATICA
nmax = 33; CoefficientList[Series[Product[1/(1 + Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 33; CoefficientList[Series[Exp[Sum[Sum[(-1)^k Prime[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (-Prime[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 33}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 13 2018
STATUS
approved