The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A052875 E.g.f.: (exp(x)-1)^2/(2-exp(x)). 10
 0, 0, 2, 12, 74, 540, 4682, 47292, 545834, 7087260, 102247562, 1622632572, 28091567594, 526858348380, 10641342970442, 230283190977852, 5315654681981354, 130370767029135900, 3385534663256845322, 92801587319328411132, 2677687796244384203114, 81124824998504073881820 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Previous name was: A simple grammar. Stirling transform of A005359(n-1)=[0,0,2,0,24,0,...] is a(n-1)=[0,0,2,12,74,...]. - Michael Somos, Mar 04 2004 Stirling transform of -(-1)^n*A052566(n-1)=[1,-1,4,-6,48,...] is a(n-1)=[1,0,2,12,74,...]. - Michael Somos, Mar 04 2004 Stirling transform of A000142(n)=[0,2,6,24,120,...] is a(n)=[0,2,12,74,...]. - Michael Somos, Mar 04 2004 Stirling transform of A007680(n)=[2,10,42,216,...] is a(n+1)=[2,12,74,...]. - Michael Somos, Mar 04 2004 a(n) is the number of chains in the power set of {1,2,...,n} that do not contain the empty set and do not contain {1,2,...,n}. Equivalently, a(n) is the number of ordered set partitions of {1,2,...,n} into at least 2 classes. - Geoffrey Critzer, Sep 01 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 846 R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1991), 23-31. Wikipedia, Ordered Bell number FORMULA Second column of A084416: Sum_{i=2..n} i!*Stirling2(n, i) = A000670(n)-1. - Vladeta Jovovic, Sep 15 2003 E.g.f.: (exp(x)-1)^2/(2-exp(x)). a(n) ~ n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Feb 25 2014 E.g.f.: A(x)*(1/(1 - A(x)) - 1) where A(x)=exp(x)-1. - Geoffrey Critzer, Sep 01 2014 EXAMPLE a(3) = 12 because we have: {{1}}, {{2}}, {{3}}, {{1,2}}, {{1,3}}, {{2,3}}, {{1}, {1,2}}, {{1}, {1,3}}, {{2}, {1,2}}, {{2}, {2,3}}, {{3}, {1,3}}, {{3}, {2,3}}. - Geoffrey Critzer, Sep 01 2014 MAPLE spec := [S, {B = Set(Z, 1 <= card), C = Sequence(B, 1 <= card), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA CoefficientList[Series[(E^x-1)^2/(2-E^x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 25 2014 *) PROG (PARI) a(n)=if(n<0, 0, n!*polcoeff(subst(y^2/(1-y), y, exp(x+x*O(x^n))-1), n)) (Sage) def A052875(n): return add(add((-1)^(j-i)*binomial(j, i)*i^n for i in range(n+1)) for j in range(n+1)) - 1 [A052875(n) for n in range(19)] # Peter Luschny, Jul 22 2014 CROSSREFS Cf. A007047, A038719. Sequence in context: A370242 A352373 A006936 * A037725 A037620 A198474 Adjacent sequences: A052872 A052873 A052874 * A052876 A052877 A052878 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS New name using e.g.f., Vaclav Kotesovec, Feb 25 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)