A047166 Number of nonempty subsets of {1,2,...,n} in which exactly 2/5 of the elements are <= n/2.

0, 0, 0, 0, 1, 3, 12, 24, 60, 100, 205, 315, 630, 980, 2156, 3528, 8260, 13692, 31620, 51600, 115995, 186945, 418825, 675675, 1535391, 2492919, 5728086, 9324406, 21448791, 34860553, 80006668, 129804808, 298009048, 483483128, 1113181012, 1807560972, 4172914197

Offset

1,6

Links

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

Formula

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

Prog

(PARI) a(n) = {my(m=n\2); sum(k=1, (n-m)\3, binomial(m, 2*k)*binomial(n-m, 3*k))} \\ Andrew Howroyd, Apr 11 2021

Crossrefs

Cf. A047165.

Sequence in context: A319422 A272173 A028725 * A076506 A206917 A320334

Adjacent sequences: A047163 A047164 A047165 * A047167 A047168 A047169

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved