A303588 Number of partitions of n that contain exactly two isolated singletons.

1, 0, 2, 2, 7, 12, 32, 67, 169, 390, 985, 2412, 6209, 15871, 41867, 110797, 299836, 817612, 2268640, 6354409, 18058764, 51838340, 150704087, 442550971, 1314527780, 3943140077, 11953192954, 36580095663, 113048257691, 352564213025, 1109727658303

Offset

2,3

Links

Table of n, a(n) for n=2..32.

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, 2), n=2..40)];

Crossrefs

Cf. A303586, A303587.

Sequence in context: A024309 A047756 A047767 * A366583 A366584 A019144

Adjacent sequences: A303585 A303586 A303587 * A303589 A303590 A303591

Keyword

nonn

Author

N. J. A. Sloane, May 19 2018

Status

approved