%I M2227 #29 Dec 27 2017 10:41:42
%S 0,1,1,1,3,1,6,1,10,4,12,1,33,1,29,13,64,1,100,1,156,30,187,1,443,10,
%T 476,78,877,1,1326,1,2098,188,2745,36,5203,1,6408,477,11084,1,15687,1,
%U 24709,1241,33249,1,57432,27,74529,2746,120984,1,168668,194,264075,6409,356624,1,579893,1,768857,14898,1214452,483,1669060,1
%N Number of set-like atomic species of degree n.
%D G. Labelle and P. Leroux, Identities and enumeration: weighting connected components, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Joerg Arndt, <a href="/A007650/b007650.txt">Table of n, a(n) for n = 0..100</a>
%H S. Eberhart & N. J. A. Sloane, <a href="/A007650/a007650.pdf">Correspondence, 1977</a>
%H G. Labelle and P. Leroux, <a href="/A007649/a007649.pdf">Identities and enumeration: weighting connected components</a>, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896. (Annotated scanned copy)
%H G. Labelle and P. Leroux, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v3i2r12">An extension of the exponential formula in enumerative combinatorics</a>, The Electronic Journal of Combinatorics, Volume 3, Issue 2 (1996) (The Foata Festschrift volume), Research Paper #R12.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Inverse Euler Transform of A007649. Define c(n): c(0)=0. c(k)=A007649(k), k>0. a=MOEBIUSi(c)-c. - _Christian G. Bower_, Feb 23 2006
%t NN = 66; va = Array[0&, NN]; va[[1]] = 0; va[[2]] = 1; vm = Array[0&, NN]; vm[[1]] = 1; vm[[2]] = 1; For[n = 2, n <= NN - 1, n++, va[[n + 1]] = DivisorSum[n , vm[[#+1]]&]; vm[[n+1]] = 1/n*Sum[DivisorSum[k, #*va[[#+1]] &]*vm[[n-k+1]], {k, 1, n}]]; va (* _Jean-François Alcover_, Dec 01 2015, adapted from _Joerg Arndt_'s PARI script in A007649 *)
%o (PARI) /* see A007649 */
%Y Cf. A005226, A007649.
%K nonn
%O 0,5
%A _Simon Plouffe_
%E Added more terms, _Joerg Arndt_, Jul 30 2012