A303587 - OEIS

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

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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