A047169 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= n/2.

0, 0, 0, 0, 0, 0, 0, 0, 4, 5, 30, 36, 126, 147, 392, 448, 1008, 1134, 2304, 2565, 5115, 5687, 12342, 13860, 34320, 39039, 104104, 119119, 315679, 360815, 913640, 1039808, 2508928, 2842604, 6651624, 7515054, 17505954, 19773414, 46915104, 53093125, 129385725, 146794494

Offset

1,9

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A047161, A047162, A047170.

Sequence in context: A266075 A041273 A256623 * A262034 A124482 A265709

Adjacent sequences: A047166 A047167 A047168 * A047170 A047171 A047172

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved