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A005461
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Number of simplices in barycentric subdivision of n-simplex.
(Formerly M4985)
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5
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1, 15, 180, 2100, 25200, 317520, 4233600, 59875200, 898128000, 14270256000, 239740300800, 4249941696000, 79332244992000, 1556132497920000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| a(n) = n(n + 1)(n + 3)!/48.
Essentially Stirling numbers of second kind - see A028246.
If we define f(n,i,x)= sum(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n-3)=(-1)^n*f(n,4,-3), (n>=4). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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MAPLE
| a:=n->sum((n-j)*n!/4!, j=3..n): seq(a(n), n=4..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
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PROG
| sage: [factorial(m+1)*binomial(m-1, 2)/24 for m in xrange (3, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008
(Other) sage: [binomial(n, 4)*factorial (n-2)/2 for n in xrange(4, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
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CROSSREFS
| Sequence in context: A001717 A004992 A055084 * A138443 A016158 A193701
Adjacent sequences: A005458 A005459 A005460 * A005462 A005463 A005464
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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