A007182 Dimension of n-th compound of a certain space.

1, 2, 5, 10, 23, 45, 94, 179, 358, 672, 1292, 2382, 4470, 8132, 14937, 26832, 48507, 86205, 153717, 270507, 476896, 832001, 1452283, 2513705, 4350072, 7475915, 12838338, 21919846, 37385434, 63450376, 107547996, 181525120, 305951060, 513772849, 861463730

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

References

• Y. Chiricota, Équations différentielles combinatoires et calcul symbolique in "FPSAC5": Formal Power Series and Algebraic Combinatorics, Fifth Conference, Florence, Jun 21-25 1993, Vol. 2, p. 123.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(d<2, d, `if`(d::odd, 0, b(d/2)))*d,
       d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
    end:
a:= n-> b(2*n):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015

Mathematica

b[n_] := b[n] = If[n==0, 1, Sum[Sum[If[d<2, d, If[OddQ[d], 0, b[d/2]]]*d, {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; a[n_] := b[2*n]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

Extensions

a(0), a(17)-a(34) from Alois P. Heinz, Jul 08 2015