A060094 Number of 6-block ordered bicoverings of an unlabeled n-set.
0, 0, 0, 0, 90, 1716, 11350, 49860, 173745, 519345, 1389078, 3411060, 7821950, 16949910, 35013240, 69404416, 132703770, 245767890, 442372300, 776064960, 1330117230, 2231754820, 3672227850, 5934754020, 9432962515, 14763202395
Offset: 0
Keywords
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
Programs
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PARI
a(n) = if(n<1, 0, binomial(n + 14, n) - 6*binomial(n + 9, 9) - 15*binomial(n + 6, 6) + 30*binomial(n + 5, 5) + 60*binomial(n + 3, 3) - 50*binomial(n + 2, 2) - 180*binomial(n + 1, 1) + 240*binomial(n, 0) - 80*binomial(n - 1, -1)) \\ Harry J. Smith, Jul 01 2009
Formula
a(n) = binomial(n+14, n) - 6*binomial(n+9, 9) - 15*binomial(n+6, 6) + 30*binomial(n+5, 5) + 60*binomial(n+3, 3) - 50*binomial(n+2, 2) - 180*binomial(n+1, 1) + 240*binomial(n, 0) - 80*binomial(n-1, -1).
G.f.: -y^4*(366*y - 16950*y^8 + 36420*y^7 - 54120*y^6 + 56290*y^5 - 40335*y^4 + 18840*y^3 - 4940*y^2 - 960*y^10 + 80*y^11 + 5220*y^9 + 90)/(-1 + y)^15.
E.g.f. for k-block ordered bicoverings of an unlabeled n-set is exp(-x - x^2/2*y/(1 - y))*Sum_{k>=0} 1/(1 - y)^binomial(k, 2)*x^k/k!.