|
Search: id:A001755
|
|
|
| A001755 |
|
Lah numbers: n!C(n-1,3)/4!.
(Formerly M5096 N2207)
|
|
+0
4
|
|
| 1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000, 1038874636800, 19833061248000, 396661224960000, 8299373322240000, 181400588328960000, 4135933413900288000, 98228418580131840000
(list; graph; listen)
|
|
|
OFFSET
|
4,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
|
|
FORMULA
|
E.g.f.: ((x/(1-x))^4)/4!.
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)^n*f(n,4,-4), (n>=4). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
|
|
MAPLE
|
A001755 := n-> n!*binomial(n-1, 3)/4!;
|
|
PROGRAM
|
(Other) sage: [binomial(n, 4)*factorial (n-1)/6 for n in xrange(4, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
|
|
CROSSREFS
|
Column 4 of A008297. Cf. A053495.
Column m=4 of unsigned triangle A111596.
Sequence in context: A077758 A053541 A004345 this_sequence A016190 A016188 A006300
Adjacent sequences: A001752 A001753 A001754 this_sequence A001756 A001757 A001758
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/12/01
|
|
|
Search completed in 0.002 seconds
|
