A001778 Lah numbers: a(n) = n!*binomial(n-1,5)/6!. (Formerly M5279 N2297)

1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800, 87265469491200, 2157837063782400, 55024845126451200, 1447576694865100800, 39291367432052736000, 1100158288097476608000, 31767070568814637056000

Offset

6,2

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 = 6..100

Formula

E.g.f.: ((x/(1-x))^6)/6!.

If we define f(n,i,x) = Sum_{k=i..n} (Sum_{j=i..k} (binomial(k,j)*Stirling1(n,k) *Stirling2(j,i)*x^(k-j) ) ) 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

From Amiram Eldar, May 02 2022: (Start)

Sum_{n>=6} 1/a(n) = 570*(gamma - Ei(1)) + 1380*e - 2999, where gamma = A001620, Ei(1) = A091725 and e = A001113.

Sum_{n>=6} (-1)^n/a(n) = 15030*(gamma - Ei(-1)) - 9000/e - 8661, where Ei(-1) = -A099285. (End)

Maple

A001778 := proc(n)
    n!*binomial(n-1, 5)/6! ;
end proc:
seq(A001778(n), n=6..30) ; # R. J. Mathar, Jan 06 2021

Mathematica

With[{c=6!}, Table[n!Binomial[n-1, 5]/c, {n, 6, 24}]] (* Harvey P. Dale, May 25 2011 *)

Prog

(Sage) [binomial(n, 6)*factorial(n-1)/factorial(5) for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009
(Magma) [Factorial(n-6)*Binomial(n, 6)*Binomial(n-1, 5): n in [6..30]]; // G. C. Greubel, May 10 2021

Crossrefs

Column 6 of A008297.

Column m=6 of unsigned triangle A111596.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A264178 A260584 A004373 * A111780 A075922 A230939

Adjacent sequences: A001775 A001776 A001777 * A001779 A001780 A001781

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Dec 18 2001

Status

approved