A060093 Number of 5-block ordered bicoverings of an unlabeled n-set.
0, 0, 0, 0, 125, 722, 2565, 7180, 17335, 37750, 76093, 144340, 260590, 451440, 755040, 1224964, 1935050, 2985380, 4509590, 6683720, 9736835, 13963670, 19739575, 27538060, 37951265, 51713706, 69729675, 93104700, 123181500
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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PARI
a(n) = if(n<1, 0, binomial(n + 9, 9) - 5*binomial(n + 5, 5) - 10*binomial(n + 3, 3) + 20*binomial(n + 2, 2) + 30*binomial(n + 1, 1) - 60*binomial(n, 0) + 24*binomial(n - 1, -1)) \\ Harry J. Smith, Jul 01 2009
Formula
a(n) = binomial(n+9, 9) - 5*binomial(n+5, 5) - 10*binomial(n+3, 3) + 20*binomial(n+2, 2) + 30*binomial(n+1, 1) - 60*binomial(n, 0) + 24*binomial(n-1, -1).
G.f.: y^4*(-528*y + 125 + 970*y^2 - 980*y^3 + 570*y^4 - 180*y^5 + 24*y^6)/(-1 + y)^10.
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!.
a(n) = (n-1) *(n-2) *(n-3) *(n^6 + 51*n^5 + 1165*n^4 + 15885*n^3 + 130954*n^2 + 660504*n + 1451520)/ 362880, n > 0. - R. J. Mathar, Aug 10 2017