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

0, 1, 0, 1, 1, 3, 5, 12, 24, 56, 123, 292, 682, 1667, 4079, 10288, 26159, 68026, 178823, 478659, 1296271, 3564911, 9919320, 27978084, 79816424, 230520511, 673071482, 1987599262, 5930739339, 17883932293, 54464027956, 167512285647, 520076498672, 1629804156975

Offset: 1

Author

N. J. A. Sloane, May 19 2018

Keywords

• nonn

Links

• A. O. Munagi, Set partitions with isolated singletons, Am. Math. Monthly 125 (2018), 447-452.

Crossrefs

Cf. A211694, A303588.

Programs

Maple

f:=proc(n,r) local j;
add(combinat:-bell(j-1)*binomial(n-j-1,j-r-1),j=1..floor((n+r)/2));
end;
[seq(f(n,1),n=1..40)];