OFFSET
1,2
FORMULA
G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 - x)) * (A(x) + Sum_{k>=1} A(x^k))).
a(n) ~ c * 3^n, where c = 0.292080665386646518390576592052254840432101999262173908555857806023213143845... - Vaclav Kotesovec, Mar 25 2020
MATHEMATICA
a[1] = 1; a[n_] := a[n] = Sum[Ceiling[n/k] a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 29}]
terms = 29; A[_] = 0; Do[A[x_] = x (1 + (1/(1 - x)) (A[x] + Sum[A[x^k], {k, 1, terms}])) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 24 2020
STATUS
approved