A333494 a(1) = 1; a(n) = Sum_{k=1..n-1} ceiling(n/k) * a(k).

1, 2, 7, 22, 69, 208, 634, 1903, 5734, 17210, 51702, 155107, 465561, 1396684, 4190689, 12572144, 37718360, 113155081, 339471195, 1018413586, 3055258062, 9165774828, 27497376189, 82492128568, 247476542954, 742429628932, 2227289352360, 6681868062822, 20045605585809

Offset: 1

Author

Ilya Gutkovskiy, Mar 24 2020

Keywords

• nonn

Crossrefs

Cf. A006590, A014668, A126656, A332846.

Programs

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

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