A097438 - OEIS

%I #12 Jul 26 2015 18:50:08

%S 0,1,1,1,2,2,5,5,14,19,37,37,146,146,317,537,1342,1342,4312,4312,

%T 13751,19648,34768,34768,178350,205852,405518,665796,1626743,1626743,

%U 6019892,6019892,19591134,26897442,48289540,68463039,270214317,270214317

%N a(n) = Sum_{k|n} a(k) a(n-k) for n >= 2, a(0)=0, a(1)=1.

%C If k in the sum in the definition is taken only over the proper divisors of n, the sequence is the same.

%C a(p) = a(p-1) if p is a prime. - _Robert G. Wilson v_, Aug 23 2004

%H Alois P. Heinz, <a href="/A097438/b097438.txt">Table of n, a(n) for n = 0..1000</a>

%e a(8) = a(1)*a(7) + a(2)*a(6) + a(4)*a(4) + a(8)*a(0) = 5 + 5 + 4 + 0 = 14.

%p a:= proc(n) option remember; `if`(n<2, n, add(

%p       a(d)*a(n-d), d=numtheory[divisors](n) minus {n}))

%p     end:

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Jul 26 2015

%t a[0] = 0; a[1] = 1; a[n_] := a[n] = Block[{d = Drop[ Divisors[n], -1]}, Plus @@ Flatten[(a /@ d)*(a /@ (n - d))]]; Table[ a[n], {n, 0, 38}] (* _Robert G. Wilson v_, Aug 23 2004 *)

%K nonn

%O 0,5

%A _Leroy Quet_, Aug 22 2004

%E More terms from _Robert G. Wilson v_, Aug 23 2004