A047165 Number of nonempty subsets of {1,2,...,n} in which exactly 1/5 of the elements are <= n/2.

0, 0, 0, 0, 0, 0, 3, 4, 20, 25, 75, 90, 210, 245, 511, 588, 1260, 1458, 3510, 4125, 10725, 12705, 32835, 38830, 96382, 113399, 273273, 320411, 770315, 903175, 2208115, 2594540, 6451500, 7594920, 18990768, 22366458, 55715562, 65579982, 162488703, 191126529

Offset

1,7

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), 4*k). - Andrew Howroyd, Apr 11 2021

Prog

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

Crossrefs

Cf. A047161, A047166, A047167, A047168.

Sequence in context: A336619 A240970 A333320 * A124631 A262033 A062870

Adjacent sequences: A047162 A047163 A047164 * A047166 A047167 A047168

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved