OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..500
N. J. A. Sloane, Transforms
FORMULA
Shifts left under Euler transform.
a(n) ~ c * d^n / n^(3/2), where d = 4.58859196701042554480382685... and c = 0.5102557157321640697473838... - Vaclav Kotesovec, Mar 29 2014
G.f. A(x) satisfies: A(x) = 2*x + x * exp( Sum_{k>=1} A(x^k) / k ). - Ilya Gutkovskiy, May 19 2023
MAPLE
with(numtheory): a:= proc(n) option remember; local d, j; if n<=1 then 3*n else (add(d*a(d), d=divisors(n-1)) +add(add(d*a(d), d=divisors(j)) *a(n-j), j=1..n-2))/ (n-1) fi end: seq(a(n), n=1..30); # Alois P. Heinz, Sep 06 2008
MATHEMATICA
a[n_] := a[n] = If[n<=1, 3*n, (Sum[d*a[d], {d, Divisors[n-1]}] + Sum[Sum[ d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-2}])/(n-1)]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 21 2016 *)
CROSSREFS
KEYWORD
nonn,easy,eigen
AUTHOR
STATUS
approved