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

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).

Links

T. D. Noe, Table of n, a(n) for n = 5..100

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.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A075911 A001719 A004359 * A205828 A353115 A136661

Adjacent sequences: A001774 A001775 A001776 * A001778 A001779 A001780

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved