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A001755 Lah numbers: a(n) = n! * binomial(n-1, 3)/4!.
(Formerly M5096 N2207)
8
1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000, 1038874636800, 19833061248000, 396661224960000, 8299373322240000, 181400588328960000, 4135933413900288000, 98228418580131840000, 2426819753156198400000, 62288373664342425600000 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,2
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
FORMULA
E.g.f.: ((x/(1-x))^4)/4!.
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,4,-4), (n>=4). - Milan Janjic, Mar 01 2009
D-finite with recurrence (-n+4)*a(n) +n*(n-1)*a(n-1)=0. - R. J. Mathar, Jan 06 2021
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=4} 1/a(n) = 12*(Ei(1) - gamma + 2*e) - 80, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=4} (-1)^n/a(n) = 156*(gamma - Ei(-1)) - 96/e - 88, where Ei(-1) = -A099285. (End)
MAPLE
A001755 := n-> n!*binomial(n-1, 3)/4!;
MATHEMATICA
Table[n!Binomial[n-1, 3]/4!, {n, 4, 25}] (* T. D. Noe, Aug 10 2012 *)
PROG
(Sage) [binomial(n, 4)*factorial (n-1)/6 for n in range(4, 21)] # Zerinvary Lajos, Jul 07 2009
(Magma) [Factorial(n-1)*Binomial(n, 4)/6: n in [4..30]]; // G. C. Greubel, May 10 2021
CROSSREFS
Column 4 of A008297.
Column m=4 of unsigned triangle A111596.
Cf. A053495.
Sequence in context: A202270 A053541 A004345 * A361577 A016190 A016188
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 12 2001
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)