%I M1381 #20 Feb 24 2016 04:36:04
%S 1,2,5,10,23,45,94,179,358,672,1292,2382,4470,8132,14937,26832,48507,
%T 86205,153717,270507,476896,832001,1452283,2513705,4350072,7475915,
%U 12838338,21919846,37385434,63450376,107547996,181525120,305951060,513772849,861463730
%N Dimension of n-th compound of a certain space.
%D 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A007182/b007182.txt">Table of n, a(n) for n = 0..1000</a>
%p b:= proc(n) option remember; `if`(n=0, 1, add(add(
%p `if`(d<2, d, `if`(d::odd, 0, b(d/2)))*d,
%p d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
%p end:
%p a:= n-> b(2*n):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, Jul 08 2015
%t 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_ *)
%K nonn
%O 0,2
%A _Simon Plouffe_
%E a(0), a(17)-a(34) from _Alois P. Heinz_, Jul 08 2015