%I #27 May 20 2021 08:19:38
%S 1,2,8,59,652,9736,186478,4421018,126317785,4260664251,166884941780,
%T 7489637988545,380861594219460,21739310882945458,1381634777325000263,
%U 97089956842985393297,7497783115765911443879,632884743974716421132084
%N Number of unordered collections of distinct nonempty subsets of an n-element set where each element appears in at most 2 subsets.
%C If each element must appear in exactly 1 subset, then we get the Bell numbers A000110.
%C If each element must appear in exactly 2 subsets, then we get A002718.
%H Alois P. Heinz, <a href="/A178165/b178165.txt">Table of n, a(n) for n = 0..300</a>
%F Binomial transform of A094574: a(n) = Sum_{k=0..n} C(n,k)*A094574(k).
%t terms = m = 30;
%t a094577[n_] := Sum[Binomial[n, k]*BellB[2n-k], {k, 0, n}];
%t egf = Exp[(1 - Exp[x])/2]*Sum[a094577[n]*(x/2)^n/n!, {n, 0, m}] + O[x]^m;
%t A094574 = CoefficientList[egf + O[x]^m, x]*Range[0, m-1]!;
%t a[n_] := Sum[Binomial[n, k]*A094574[[k+1]], {k, 0, n}];
%t Table[a[n], {n, 0, m-1}] (* _Jean-François Alcover_, May 24 2019 *)
%o (Python)
%o def powerSet(k): return [toBinary(n,k) for n in range(1,2**k)]
%o def courcelle(maxUses, remainingSets, exact=False):
%o if exact and not all(maxUses<=sum(remainingSets)): ans=0
%o elif len(remainingSets)==0: ans=1
%o else:
%o set0=remainingSets[0]
%o if all(set0<=maxUses): ans=courcelle(maxUses-set0,remainingSets[1:],exact=exact)
%o else: ans=0
%o ans+=courcelle(maxUses,remainingSets[1:],exact=exact)
%o return ans
%o for i in range(10):
%o print(i, courcelle(array([2]*i),powerSet(i),exact=False))
%Y Row n=2 of A330964.
%Y Cf. A094574, A000110, A002718, A178171, A178173.
%K nonn
%O 0,2
%A _Daniel E. Loeb_, Dec 16 2010
%E Edited and corrected by _Max Alekseyev_, Dec 19 2010