OFFSET
0,3
FORMULA
a(n) ~ exp(2*sqrt(n/5) - 1/10 + c/5) * 5^(n - 1/4) / (2*sqrt(Pi)*n^(3/4)), where c = Sum_{j>=2} 1/(j * (5^(j-1) - 1)). - Vaclav Kotesovec, Apr 12 2021
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
d*5^(d-1), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..24); # Alois P. Heinz, Apr 12 2021
MATHEMATICA
nmax = 24; CoefficientList[Series[Product[1/(1 - x^k)^(5^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 5^(d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 12 2021
STATUS
approved