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A054559
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Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 8 1-simplexes.
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4
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30, 180, 630, 1680, 3780, 7560, 13860, 23760, 38610, 60060, 90090, 131040, 185640, 257040, 348840, 465120, 610470, 790020, 1009470, 1275120, 1593900, 1973400, 2421900, 2948400, 3562650, 4275180
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,1
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COMMENTS
| 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=8.
Let H be the n-by-n Hilbert matrix H(i,j) = 1/(i+j-1) for 1 <= i,j <= n. Let B be the inverse matrix of H. The sum of the elements in row 3 of B equals -a(n+2). - T. D. Noe, May 01 2011
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REFERENCES
| 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.
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FORMULA
| a(n) = 30*C(n,5) = n*(n-1)*(n-2)*(n-3)*(n-4)/4.
G.f.: 30*x^5/(1-x)^6. [Colin Barker, Jan 19 2012]
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MATHEMATICA
| Table[n*(n+1)*(n+2)*(n+3)*(n+4)/4, {n, 0, 100}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 21 2009]
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CROSSREFS
| Cf. A054557.
Cf. A000389, A052787.
Sequence in context: A159653 A101098 A068236 * A042756 A156318 A042758
Adjacent sequences: A054556 A054557 A054558 * A054560 A054561 A054562
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2000
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