A047170 Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= n/2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 6, 36, 42, 147, 168, 448, 504, 1134, 1260, 2565, 2827, 5687, 6270, 13860, 15444, 39039, 44044, 119119, 135135, 360815, 408968, 1039808, 1174224, 2842604, 3197904, 7515054, 8436114, 19773414, 22203020, 53093125, 59750649, 146794494

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A047169.

Programs

PARI

a(n) = {my(m=n\2); sum(k=1, m\5, binomial(m, 5*k)*binomial(n-m, k))} \\ Andrew Howroyd, Apr 11 2021

Formula

a(n) = Sum_{k>=1} binomial(floor(n/2), 5*k)*binomial(ceiling(n/2), k). - Andrew Howroyd, Apr 11 2021

Extensions

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