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A097438
a(n) = Sum_{k|n} a(k) a(n-k) for n >= 2, a(0)=0, a(1)=1.
1
0, 1, 1, 1, 2, 2, 5, 5, 14, 19, 37, 37, 146, 146, 317, 537, 1342, 1342, 4312, 4312, 13751, 19648, 34768, 34768, 178350, 205852, 405518, 665796, 1626743, 1626743, 6019892, 6019892, 19591134, 26897442, 48289540, 68463039, 270214317, 270214317
OFFSET
0,5
COMMENTS
If k in the sum in the definition is taken only over the proper divisors of n, the sequence is the same.
a(p) = a(p-1) if p is a prime. - Robert G. Wilson v, Aug 23 2004
LINKS
EXAMPLE
a(8) = a(1)*a(7) + a(2)*a(6) + a(4)*a(4) + a(8)*a(0) = 5 + 5 + 4 + 0 = 14.
MAPLE
a:= proc(n) option remember; `if`(n<2, n, add(
a(d)*a(n-d), d=numtheory[divisors](n) minus {n}))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jul 26 2015
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A098887 A259097 A245845 * A205482 A055879 A056470
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 22 2004
EXTENSIONS
More terms from Robert G. Wilson v, Aug 23 2004
STATUS
approved