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A001777 Lah numbers: n! * binomial(n-1, 4)/5!.
(Formerly M5213 N2267)
8

%I M5213 N2267

%S 1,30,630,11760,211680,3810240,69854400,1317254400,25686460800,

%T 519437318400,10908183686400,237996734976000,5394592659456000,

%U 126980411830272000,3101950060425216000,78582734864105472000,2062796790182768640000,56059536297908183040000

%N Lah numbers: n! * binomial(n-1, 4)/5!.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001777/b001777.txt">Table of n, a(n) for n = 5..100</a>

%F E.g.f.: ((x/(1-x))^5)/5!.

%F 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)=(-1)^n*f(n,4,-6), (n>=4). - _Milan Janjic_, Mar 01 2009

%p A001777 := n-> n!*binomial(n-1,4)/5!;

%t Table[n! Binomial[n - 1, 4]/5!, {n, 5, 20}] (* _T. D. Noe_, Aug 10 2012 *)

%o (Sage) [binomial(n,5)*factorial (n-1)/factorial (4) for n in range(5, 21)] # _Zerinvary Lajos_, Jul 07 2009

%Y Column 5 of A008297. Cf. A053495.

%Y Column m=5 of unsigned triangle A111596.

%K nonn,easy

%O 5,2

%A _N. J. A. Sloane_

%E More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu)

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)