A047162 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= n/2.

0, 0, 0, 2, 3, 9, 12, 30, 40, 100, 135, 335, 455, 1127, 1540, 3822, 5250, 13050, 18000, 44802, 62007, 154517, 214467, 534963, 744315, 1858155, 2590679, 6472167, 9039823, 22597759, 31612324, 79067374, 110761494, 277164294, 388742706, 973184312, 1366460867, 3422117189

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{k>=1} binomial(floor(n/2), 2*k)*binomial(ceiling(n/2), k). - Andrew Howroyd, Apr 11 2021

Prog

(PARI) a(n) = {my(m=n\2); sum(k=1, n\4, binomial(m, 2*k)*binomial(n-m, k))} \\ Andrew Howroyd, Apr 11 2021

Crossrefs

Cf. A047161.

Sequence in context: A330298 A330242 A239859 * A155929 A175206 A032486

Adjacent sequences: A047159 A047160 A047161 * A047163 A047164 A047165

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(35) and beyond from Andrew Howroyd, Apr 11 2021

Status

approved