Search: id:A001192
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%I A001192 M1951 N0772
%S A001192 1,1,1,2,9,88,1802,75598,6421599,1097780312,376516036188,258683018091900,
%T A001192 355735062429124915,978786413996934006272,5387230452634185460127166,
%U A001192 59308424712939278997978128490,1305926814154452720947815884466579
%N A001192 Number of full sets of size n.
%C A001192 A set x is full if every element of x is also a subset of x.
%C A001192 Equals the subpartitions of Eulerian numbers (A000295(n)=2^n-n-1); see 
               A115728 for the definition of subpartitions of a partition. - Paul 
               D. Hanna (pauldhanna(AT)juno.com), Jul 03 2006
%D A001192 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001192 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001192 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 123, Problem 20.
%D A001192 R. Peddicord, The number of full sets with n elements, Proc. Amer. Math. 
               Soc., 13 (1962), 825-828.
%F A001192 1 = Sum_{n>=0} a(n)*x^n/(1+x)^(2^n). E.g. 1 = 1/(1+x) + 1*x/(1+x)^2 + 
               1*x^2/(1+x)^4 + 2*x^3/(1+x)^8 + 9*x^4/(1+x)^16 + 88*x^5/(1+x)^32 
               + 1802*x^6/(1+x)^64 +... - Vladeta Jovovic, May 26 2005
%F A001192 Equivalently, a(n) = (-1)^n*C(2^n+n-1, n) - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(2^n+2^k+n-k-1, 
               n-k). - Paul Hanna, May 26 2005
%F A001192 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n*(1-x)^(2^n-n-1) = 1*(1-x)^0 + 1*x*(1-x)^0 
               + 1*x^2*(1-x)^1 + 2*x^3*(1-x)^4 + 9*x^3*(1-x)^11 +...+ a(n)*x^n*(1-x)^(2^n-n-1) 
               +... - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 03 2006
%e A001192 Examples of full sets are 0 := {}, 1 := {0}, 2 := {1,0}, 3a := {2,1,0}, 
               3b := { {1}, 1, 0}, 4a := { 3a, 2, 1, 0 }.
%o A001192 (PARI) {a(n)=polcoeff(x^n-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(2^k-k-1) 
               ), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 03 2006
%Y A001192 Cf. A115728, A000295.
%Y A001192 Sequence in context: A037172 A135747 A132431 this_sequence A006120 A012941 
               A059477
%Y A001192 Adjacent sequences: A001189 A001190 A001191 this_sequence A001193 A001194 
               A001195
%K A001192 nonn,nice
%O A001192 0,4
%A A001192 N. J. A. Sloane (njas(AT)research.att.com).
%E A001192 More terms from Ryan Propper (rpropper(AT)stanford.edu), Jun 13 2005

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