A060091 Number of 4-block ordered bicoverings of an unlabeled n-set.
0, 0, 0, 16, 63, 162, 341, 636, 1092, 1764, 2718, 4032, 5797, 8118, 11115, 14924, 19698, 25608, 32844, 41616, 52155, 64714, 79569, 97020, 117392, 141036, 168330, 199680, 235521, 276318, 322567, 374796, 433566, 499472, 573144, 655248, 746487
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1)
Programs
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PARI
a(n) = if(n<1, 0, binomial(n + 5, 5) - 4*binomial(n + 2, 2) - 3*binomial(n + 1, 1) + 12*binomial(n, 0) - 6*binomial(n - 1, -1)) \\ Harry J. Smith, Jul 01 2009
Formula
a(n) = binomial(n + 5, 5) - 4*binomial(n + 2, 2) - 3*binomial(n + 1, 1) + 12*binomial(n, 0) - 6*binomial(n - 1, -1).
G.f.: - y^3*( - 24*y^2 - 16 + 33*y + 6*y^3)/( - 1 + y)^6.
E.g.f. for ordered k-block 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+5)*(n-1)*(n-2)*(n^2+13*n+72)/120, n>0. - R. J. Mathar, Aug 15 2017