A097919 a(1)=1; a(n+1) = Sum_{k=1 to n} a(k) a(ceiling(n/k)).

1, 1, 2, 5, 13, 35, 92, 246, 646, 1705, 4475, 11755, 30790, 80738, 211424, 553780, 1449999, 3796903, 9940710, 26027151, 68140743, 178399767, 467059142, 1222789414, 3201309100, 8381170779, 21942203523, 57445520528, 150394362117, 393737778753, 1030818974142

Offset: 1

Author

N. J. A. Sloane, following a suggestion of Benoit Cloitre, Sep 03 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A097417.

Programs

Maple

f:=proc(n) option remember; local k; if n = 1 then RETURN(1); fi; add( f(k)*f(ceil((n-1)/k)), k=1..n-1 ); end;

Mathematica

a[1] := 1; a[n_] := a[n] = Sum[a[k]*a[Ceiling[(n - 1)/k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 30}] (* G. C. Greubel, Dec 20 2017 *)

Formula

a(n) ~ c * ((3 + sqrt(5))/2)^n, where c = 0.113749340218250534902880196020226926353440247305682768150354123166912... - Vaclav Kotesovec, Feb 26 2020