A097438 a(n) = Sum_{k|n} a(k) a(n-k) for n >= 2, a(0)=0, a(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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A097435 A097436 A097437 * A097439 A097440 A097441

Keyword

nonn

Author

Leroy Quet, Aug 22 2004

Extensions

More terms from Robert G. Wilson v, Aug 23 2004

Status

approved