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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Christian G. Bower, Dec 18 2001
STATUS
approved