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

1, 30, 630, 11760, 211680, 3810240, 69854400, 1317254400, 25686460800, 519437318400, 10908183686400, 237996734976000, 5394592659456000, 126980411830272000, 3101950060425216000, 78582734864105472000, 2062796790182768640000, 56059536297908183040000

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

Column 5 of A008297. Cf. A053495.

Column m=5 of unsigned triangle A111596.

Cf. A001113, A001620, A091725, A099285.

Programs

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 *)

Sage

[binomial(n,5)*factorial (n-1)/factorial (4) for n in range(5, 21)] # Zerinvary Lajos, Jul 07 2009

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)

Extensions

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