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Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 9 1-simplexes.
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%I #16 Jun 18 2017 02:23:08

%S 150,960,3605,10360,25200,54600,108570,201960,356070,600600,975975,

%T 1536080,2351440,3512880,5135700,7364400,10377990,14395920,19684665,

%U 26565000,35420000,46703800,60951150,78787800,100941750,128255400

%N Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 9 1-simplexes.

%C Number of {T_1,T_2,...,T_k} where T_i, i=1..k are 3-subsets of an n-set such that {D | D is 2-subset of T_i for some i=1..k} has l elements; k=5, l=9.

%D V. Jovovic, On the number of two-dimensional simplicial complexes (in Russian), Metody i sistemy tekhnicheskoy diagnostiki, Vypusk 16, Mezhvuzovskiy zbornik nauchnykh trudov, Izdatelstvo Saratovskogo universiteta, 1991.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = 150*C(n,5) +60*C(n,6) +35*C(n,7) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n^2+n+150)/144.

%F G.f.: 5*x^5*(30-48*x+25*x^2)/(1-x)^8. - _Colin Barker_, Jun 21 2012

%p A054558:=n->n*(n-1)*(n-2)*(n-3)*(n-4)*(n^2+n+150)/144; seq(A054558(n), n=5..30); # _Wesley Ivan Hurt_, Apr 29 2014

%t Table[n*(n - 1)*(n - 2)*(n - 3)*(n - 4)*(n^2 + n + 150)/144, {n, 5, 30}] (* _Wesley Ivan Hurt_, Apr 29 2014 *)

%Y Cf. A054557.

%K nonn,easy

%O 5,1

%A _Vladeta Jovovic_, Apr 10 2000