A047167 Number of nonempty subsets of {1,2,...,n} in which exactly 3/5 of the elements are <= n/2.

0, 0, 0, 0, 0, 3, 6, 24, 40, 100, 150, 315, 455, 980, 1470, 3528, 5544, 13692, 21630, 51600, 80520, 186945, 290400, 675675, 1056627, 2492919, 3929926, 9324406, 14742910, 34860553, 55107598, 129804808, 205272008, 483483128, 765991032, 1807560972, 2869786524, 6779169543

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\3, binomial(m, 3*k)*binomial(n-m, 2*k))} \\ Andrew Howroyd, Apr 11 2021

Formula

a(n) = Sum_{k>=1} binomial(floor(n/2), 3*k)*binomial(ceiling(n/2), 2*k). - Andrew Howroyd, Apr 11 2021

Extensions

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