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A001778
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Lah numbers: n!C(n-1,5)/6!.
(Formerly M5279 N2297)
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5
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1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800, 87265469491200, 2157837063782400, 55024845126451200, 1447576694865100800, 39291367432052736000, 1100158288097476608000, 31767070568814637056000
(list;
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OFFSET
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6,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 6..100
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FORMULA
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E.g.f.: ((x/(1-x))^6)/6!.
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)=(-1)^n*f(n,6,-6), (n>=6). [Milan Janjic, Mar 01 2009]
D-finite with recurrence (-n+6)*a(n) +n*(n-1)*a(n-1)=0. - R. J. Mathar, Jan 06 2021
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MAPLE
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A001778 := proc(n)
n!*binomial(n-1, 5)/6! ;
end proc:
seq(A001778(n), n=6..30) ; # R. J. Mathar, Jan 06 2021
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MATHEMATICA
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With[{c=6!}, Table[n!Binomial[n-1, 5]/c, {n, 6, 24}]] (* Harvey P. Dale, May 25 2011 *)
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PROG
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(Sage) [binomial(n, 6)*factorial (n-1)/factorial (5) for n in range(6, 22)] # [Zerinvary Lajos, Jul 07 2009]
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CROSSREFS
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Column 6 of A008297.
Column m=6 of unsigned triangle A111596.
Sequence in context: A264178 A260584 A004373 * A111780 A075922 A230939
Adjacent sequences: A001775 A001776 A001777 * A001779 A001780 A001781
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Christian G. Bower, Dec 18 2001
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STATUS
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approved
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