OFFSET
1,4
REFERENCES
S. M. Kerawala, The asymptotic number of three-deep Latin rectangles, Bull. Calcutta Math. Soc., 39 (1947), 71-72.
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
S. M. Kerawala, The asymptotic number of three-deep Latin rectangles, Bull. Calcutta Math. Soc., 39 (1947), 71-72. [Annotated scanned copy]
S. M. Kerawala, Asymptotic solution of the "Probleme des menages, Bull. Calcutta Math. Soc., 39 (1947), 82-84. [Annotated scanned copy]
PROG
(Sage)
def A001568(N):
a = polygen(QQ, 'a')
R = PowerSeriesRing(a.parent(), 't', default_prec=N + 2)
t = R.gen()
n = 1 / t
dico = {0: 1}
for k in range(1, N + 1):
U = sum(di * t**i / factorial(i) for i, di in dico.items())
U += a * t**k / factorial(k)
U = U.O(k + 2)
delta = -U+(n-1)*(n**2-2*n+2)/n**2/(n-2)*U(t=1/(n-1))+(n**2-2*n+2)/n**2/(n-1)*U(t=1/(n-2))+(n**2-2*n-2)/n**2/(n-1)/(n-2)**2*U(t=1/(n-3))+2*(n*n-5*n+3)/n**2/(n-1)/(n-2)**2/(n-3)*U(t=1/(n-4))-4/n**2/(n-2)**2/(n-3)/(n-4)*U(t=1/(n-5))
dico[k] = delta[k + 1].numerator().roots()[0][0]
return list(dico.values())
# F. Chapoton, Jan 01 2022
CROSSREFS
KEYWORD
sign,more
AUTHOR
EXTENSIONS
Signs added by N. J. A. Sloane, Jul 23 2015
More terms from F. Chapoton, Jan 01 2022
STATUS
approved