OFFSET
0,3
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} 1 / (1 - x^k)^(m^(k-1)), then a(n, m) ~ exp(2*sqrt(n/m) - 1/(2*m) + c(m)/m) * m^(n - 1/4) / (2*sqrt(Pi)*n^(3/4)), where c(m) = Sum_{j>=2} 1/(j * (m^(j-1) - 1)). - Vaclav Kotesovec, Apr 12 2021
FORMULA
a(n) ~ exp(sqrt(2*n/5) - 1/20 + c/10) * 10^(n - 1/4) / (2*sqrt(Pi)*n^(3/4)), where c = Sum_{j>=2} 1/(j * (10^(j-1) - 1)). - Vaclav Kotesovec, Apr 12 2021
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
d*10^(d-1), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 12 2021
MATHEMATICA
nmax = 21; CoefficientList[Series[Product[1/(1 - x^k)^(10^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 10^(d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 12 2021
STATUS
approved