A377464 Number of connected pairs of subsets of [n] with each being a different size.

0, 0, 2, 12, 62, 290, 1292, 5579, 23606, 98490, 406862, 1668689, 6807704, 27663441, 112076057, 453031502, 1828018406, 7366128866, 29650536878, 119249689265, 479277846962, 1925216817095, 7729973578307, 31025341749680, 124486445913728, 499362094315865

Offset: 0

Author

John Tyler Rascoe, Oct 29 2024

Keywords

• nonn
• easy

Comments

Empirically, a(A075930(n)) == 1 (mod 2).

Examples

			a(3) = 12 counts the pairs: {{1,2},{1}}, {{1,2},{2}}, {{1,3},{1}}, {{1,3},{3}}, {{2,3},{2}}, {{2,3},{3}}, {{1,2,3},{1,2}}, {{1,2,3},{1,3}}, {{1,2,3},{2,3}}, {{1,2,3},{1}}, {{1,2,3},{2}}, {{1,2,3},{3}}.
		

Crossrefs

Cf. A001187, A075930, A323818, A326749.

Programs

PARI

A377464(n) = {sum(i=0,n-2,binomial(n,i)*sum(j=i+1,n-1, binomial(n,j)-binomial(i,n-j)))}

Formula

a(n) = Sum_{i=0..n-2} binomial(n,i) * Sum_{j=i+1..n-1} (binomial(n,j) - binomial(i,n-j)).