Search: id:A002050
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%I A002050 M3939 N1622
%S A002050 0,1,5,25,149,1081,9365,94585,1091669,14174521,204495125,3245265145,
%T A002050 56183135189,1053716696761,21282685940885,460566381955705,
%U A002050 10631309363962709,260741534058271801,6771069326513690645
%N A002050 Number of simplices in barycentric subdivision of n-simplex.
%C A002050 Stirling transform of A052849(n)=[1,4,12,48,240,...] is a(n)=[1,5,25,
               149,1081,..]. - Michael Somos Mar 04 2004
%C A002050 Stirling transform of A000142(n-1)=[0,1,2,6,24,...] is a(n-1)=[0,1,5,
               25,149,...]. - Michael Somos Mar 04 2004
%C A002050 Stirling transform of 2*A005359(n-1)=[1,0,4,0,48,0,...] is a(n-1)=[1,
               1,5,25,149,...]. - Michael Somos Mar 04 2004
%C A002050 "Stirling-Bernoulli transform" of A000225. - Paul Barry (pbarry(AT)wit.ie), 
               Apr 20 2005
%C A002050 a(n) is the number of nonempty words that can be formed from an alphabet 
               of nonempty subsets of [n] so that the letters in each word are pairwise 
               disjoint. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Apr 12 2009]
%D A002050 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002050 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002050 G. J. Simmons, A combinatorial problem associated with a family of combination 
               locks, Math. Mag., 37 (1964), 127-132 (but there are errors).
%D A002050 J. F. Steffensen, On a class of polynomials and their application to 
               actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 
               75-97, 1928.
%H A002050 T. D. Noe, <a href="b002050.txt">Table of n, a(n) for n=0..100</a>
%H A002050 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=149">
               Encyclopedia of Combinatorial Structures 149</a>
%F A002050 E.g.f.: (exp(2x)-exp(x))/(2-exp(x)).
%F A002050 a(n)=sum{k=0..n, (-1)^(n-k)k!*S2(n, k)(2^k-1)}. - Paul Barry (pbarry(AT)wit.ie), 
               Apr 20 2005
%F A002050 a(n)= Sum{k=1...n,Binomial(n,k)*A000670(k)} [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Apr 12 2009]
%t A002050 Table[Sum[Binomial[n, i]*Sum[StirlingS2[i, k]*k!, {k, 1, i}], {i, 1, 
               n}], {n, 0, 20}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Apr 12 2009]
%o A002050 (PARI) a(n)=if(n<0,0,n!*polcoeff(subst((y+y^2)/(1-y),y,exp(x+x*O(x^n))-1),
               n))
%Y A002050 a(n) = A000629(n) - 1.
%Y A002050 Sequence in context: A121639 A098349 A098212 this_sequence A047782 A106565 
               A092166
%Y A002050 Adjacent sequences: A002047 A002048 A002049 this_sequence A002051 A002052 
               A002053
%K A002050 nonn,easy,nice
%O A002050 0,3
%A A002050 N. J. A. Sloane (njas(AT)research.att.com).
%E A002050 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000

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