cp's OEIS Frontend

A060091 Number of 4-block ordered bicoverings of an unlabeled n-set.

%I A060091 #16 Jan 30 2020 14:24:55
%S A060091 0,0,0,16,63,162,341,636,1092,1764,2718,4032,5797,8118,11115,14924,
%T A060091 19698,25608,32844,41616,52155,64714,79569,97020,117392,141036,168330,
%U A060091 199680,235521,276318,322567,374796,433566,499472,573144,655248,746487
%N A060091 Number of 4-block ordered bicoverings of an unlabeled n-set.
%H A060091 Harry J. Smith, <a href="/A060091/b060091.txt">Table of n, a(n) for n = 0..1000</a>
%H A060091 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1)
%F A060091 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).
%F A060091 G.f.: - y^3*( - 24*y^2 - 16 + 33*y + 6*y^3)/( - 1 + y)^6.
%F A060091 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!.
%F A060091 a(n) = (n+5)*(n-1)*(n-2)*(n^2+13*n+72)/120, n>0. - _R. J. Mathar_, Aug 15 2017
%o A060091 (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
%Y A060091 Column k=4 of A060092.
%Y A060091 Cf. A059945, A060090, A060488.
%K A060091 nonn,easy
%O A060091 0,4
%A A060091 _Vladeta Jovovic_, Feb 26 2001