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A001777
Lah numbers: a(n) = n! * binomial(n-1, 4)/5!.
(Formerly M5213 N2267)
8
1, 30, 630, 11760, 211680, 3810240, 69854400, 1317254400, 25686460800, 519437318400, 10908183686400, 237996734976000, 5394592659456000, 126980411830272000, 3101950060425216000, 78582734864105472000, 2062796790182768640000, 56059536297908183040000
OFFSET
5,2
REFERENCES
Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
John 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).
FORMULA
E.g.f.: ((x/(1-x))^5)/5!.
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
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=5} 1/a(n) = 20*(Ei(1) - gamma) - 200*e + 1555/3, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=5} (-1)^(n+1)/a(n) = 1460*(gamma - Ei(-1)) - 880/e - 2515/3, where Ei(-1) = -A099285. (End)
MAPLE
A001777 := n-> n!*binomial(n-1, 4)/5!;
MATHEMATICA
Table[n! Binomial[n - 1, 4]/5!, {n, 5, 20}] (* T. D. Noe, Aug 10 2012 *)
PROG
(Sage) [binomial(n, 5)*factorial (n-1)/factorial (4) for n in range(5, 21)] # Zerinvary Lajos, Jul 07 2009
CROSSREFS
Column 5 of A008297. Cf. A053495.
Column m=5 of unsigned triangle A111596.
Sequence in context: A075911 A001719 A004359 * A205828 A353115 A136661
KEYWORD
nonn,easy
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu)
STATUS
approved