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

1,6

Links

Table of n, a(n) for n=1..34.

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

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)];

Crossrefs

Cf. A303586, A303588.

Sequence in context: A185087 A090345 A186334 * A151524 A030270 A129757

Adjacent sequences: A303584 A303585 A303586 * A303588 A303589 A303590

Keyword

nonn

Author

N. J. A. Sloane, May 19 2018

Status

approved