The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A283877 Number of non-isomorphic set-systems of weight n. 171
 1, 1, 2, 4, 9, 18, 44, 98, 244, 605, 1595, 4273, 12048, 34790, 104480, 322954, 1031556, 3389413, 11464454, 39820812, 141962355, 518663683, 1940341269, 7424565391, 29033121685, 115921101414, 472219204088, 1961177127371, 8298334192288, 35751364047676, 156736154469354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A set-system is a finite set of finite nonempty sets. The weight of a set-system is the sum of cardinalities of its elements. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 FORMULA Euler transform of A300913. EXAMPLE Non-isomorphic representatives of the a(4)=9 set-systems are: ((1234)), ((1)(234)), ((3)(123)), ((12)(34)), ((13)(23)), ((1)(2)(12)), ((1)(2)(34)), ((1)(3)(23)), ((1)(2)(3)(4)). PROG (PARI) \\ SetTypes function referenced by other sequences. WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} V(n, w)={sumdiv(gcd(n, w), d, moebius(d)*binomial(n/d, w/d))/n} S(n)={my(v=vector(n)); for(w=0, n, fordiv(gcd(n, w), d, v[n/d] += x^w*V(n/d, w/d))); v} SetTypes(ptyp, fx)={ my(lim=sum(i=1, #ptyp, ptyp[i]), u=vector(lim, i, O(x*x^(lim\i)))); u[1] += 1; for(i=1, #ptyp, my(s=S(ptyp[i]), v=vector(#u)); for(j=1, #u, for(k=1, #s, my(g=lcm(j, k)); if(g<=#v, v[g]+=u[j]*s[k]*j*k/g))); u=v); u[1]-=1; Vec(sum(i=1, #u, subst(fx(u[i]), x, x^i)) + O(x*x^lim), -lim); } a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*WeighT(SetTypes(p, q->q))[n]); s/n!} \\ Andrew Howroyd, Sep 01 2019 CROSSREFS Cf. A007716, A034691, A049311, A056156, A089259, A116540, A300913. Sequence in context: A259803 A032175 A000678 * A331850 A081490 A292478 Adjacent sequences:  A283874 A283875 A283876 * A283878 A283879 A283880 KEYWORD nonn AUTHOR Gus Wiseman, Mar 17 2017 EXTENSIONS a(0) = 1 prepended and terms a(11) and beyond from Andrew Howroyd, Sep 01 2019 STATUS approved

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

Last modified May 5 19:09 EDT 2021. Contains 343573 sequences. (Running on oeis4.)