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

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, A303587.

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