A047168 Number of nonempty subsets of {1,2,...,n} in which exactly 4/5 of the elements are <= n/2.

0, 0, 0, 0, 0, 0, 0, 4, 5, 25, 30, 90, 105, 245, 280, 588, 666, 1458, 1665, 4125, 4785, 12705, 14850, 38830, 45331, 113399, 131859, 320411, 371735, 903175, 1048840, 2594540, 3021240, 7594920, 8863698, 22366458, 26122302, 65579982, 76575225, 191126529

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A047165.

Programs

PARI

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

Formula

a(n) = Sum_{k>=1} binomial(floor(n/2), 4*k)*binomial(ceiling(n/2), k). - Andrew Howroyd, Apr 11 2021

Extensions

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