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A001568
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Related to 3-line Latin rectangles.
(Formerly M2171 N0867)
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1
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1, -1, -1, 2, 49, 629, 6961, 38366, -1899687, -133065253, -6482111309, -281940658286, -10702380933551, -247708227641863, 14512103549430397, 3377044611825908414, 433180638973276282801, 47474992085447610990231
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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REFERENCES
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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).
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LINKS
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PROG
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(Sage)
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())
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CROSSREFS
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KEYWORD
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sign,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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