cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A303587 Number of partitions of n that contain exactly one isolated singleton.

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%I A303587 #7 Feb 07 2025 12:01:51
%S A303587 0,1,0,1,1,3,5,12,24,56,123,292,682,1667,4079,10288,26159,68026,
%T A303587 178823,478659,1296271,3564911,9919320,27978084,79816424,230520511,
%U A303587 673071482,1987599262,5930739339,17883932293,54464027956,167512285647,520076498672,1629804156975
%N A303587 Number of partitions of n that contain exactly one isolated singleton.
%H A303587 A. O. Munagi, <a href="https://doi.org/10.1080/00029890.2018.1430960">Set partitions with isolated singletons</a>, Am. Math. Monthly 125 (2018), 447-452.
%p A303587 f:=proc(n,r) local j;
%p A303587 add(combinat:-bell(j-1)*binomial(n-j-1,j-r-1),j=1..floor((n+r)/2));
%p A303587 end;
%p A303587 [seq(f(n,1),n=1..40)];
%Y A303587 Cf. A211694, A303588.
%K A303587 nonn
%O A303587 1,6
%A A303587 _N. J. A. Sloane_, May 19 2018