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
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..500
Crossrefs
Cf. A047165.
Programs
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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
Formula
a(n) = Sum_{k>=1} binomial(floor(n/2), 2*k)*binomial(ceiling(n/2), 3*k). - Andrew Howroyd, Apr 11 2021
Extensions
Terms a(35) and beyond from Andrew Howroyd, Apr 11 2021