OFFSET
4,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.
Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.
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 = 4..100
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Cornelius Lanczos, Applied Analysis. (Annotated scans of selected pages)
FORMULA
a(n) = n!*n*(n-1)(n-2)(n-3)/(4!)^2. a(4)=1, a(n+1) = a(n) * (n+1)^2 / (n-3).
a(n) = A021009(n, 4), n >= 4.
E.g.f.: x^4/(4!*(1-x)^5).
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,-5), (n >= 4). - Milan Janjic, Mar 01 2009
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=4} 1/a(n) = 64*(Ei(1) - gamma - e) + 272/3, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=4} (-1)^n/a(n) = 544*(gamma - Ei(-1)) - 320/e - 944/3, where Ei(-1) = -A099285. (End)
EXAMPLE
G.f. = x^4 + 25*x^5 + 450*x^6 + 7350*x^7 + 117600*x^8 + 1905120*x^9 + ...
MAPLE
with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), right=Set(U, card<r), U=Sequence(Z, card>=1)}, labeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=4..19) ; # Zerinvary Lajos, Feb 07 2008
MATHEMATICA
Table[n! n (n - 1) (n - 2) (n - 3)/(4!)^2, {n, 4, 20}] (* T. D. Noe, Aug 10 2012 *)
PROG
(Sage) [factorial(m) * binomial(m, 4) / 24 for m in range(4, 19)] # Zerinvary Lajos, Jul 05 2008
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001
Corrected by T. D. Noe, Aug 10 2012
STATUS
approved