|
%I #15 Sep 08 2022 08:44:59
%S 0,0,0,0,0,0,80,840,7896,76608,793152,8838720,106096320,1368956160,
%T 18928615680,279530334720,4394135692800,73295141068800,
%U 1293442388582400,24082259707699200,471874122729676800
%N Number of pairs of cycles of cardinality at least 3.
%H G. C. Greubel, <a href="/A052519/b052519.txt">Table of n, a(n) for n = 0..448</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=85">Encyclopedia of Combinatorial Structures 85</a>
%F E.g.f.: log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4.
%F (n-1)*a(n+2) + (3+n-2*n^2)*a(n+1) - n*(2+n-n^2)*a(n) = 0, with a(0) = .. = a(5) = 0, a(6) = 80.
%p Pairs spec := [S,{B=Cycle(Z,3 <= card),S=Prod(B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{m = 25}, CoefficientList[Series[Log[1-x]^2 +x*(2+x)*Log[1-x] +x^2 + x^3 +x^4/4, {x,0,m}], x]*Range[0, m]!] (* _G. C. Greubel_, May 13 2019 *)
%o (PARI) my(x='x+O('x^25)); concat(vector(6), Vec(serlaplace( log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4 ))) \\ _G. C. Greubel_, May 13 2019
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Log(1-x)^2 + x*(2+x)*Log(1-x) + x^2 + x^3 + x^4/4 )); [0,0,0,0,0,0] cat [Factorial(n+5)*b[n]: n in [1..m-6]]; // _G. C. Greubel_, May 13 2019
%o (Sage) m = 25; T = taylor(log(1-x)^2 + x*(2+x)*log(1-x) + x^2 + x^3 + x^4/4, x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, May 13 2019
%K easy,nonn
%O 0,7
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
