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A303587 Number of partitions of n that contain exactly one isolated singleton. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
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
Sequence in context: A185087 A090345 A186334 * A151524 A030270 A129757
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 19 2018
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)