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A001778
Lah numbers: a(n) = n!*binomial(n-1,5)/6!.
(Formerly M5279 N2297)
5
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).
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.
Sequence in context: A264178 A260584 A004373 * A111780 A075922 A230939
KEYWORD
nonn,easy
EXTENSIONS
More terms from Christian G. Bower, Dec 18 2001
STATUS
approved