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 A001568 Related to 3-line Latin rectangles. (Formerly M2171 N0867) 1
 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)
 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 Table of n, a(n) for n=1..18. 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] Index entries for sequences related to Latin squares and rectangles 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 Sequence in context: A297989 A028479 A189389 * A221134 A243720 A210922 Adjacent sequences: A001565 A001566 A001567 * A001569 A001570 A001571 KEYWORD sign,more AUTHOR N. J. A. Sloane EXTENSIONS Signs added by N. J. A. Sloane, Jul 23 2015 More terms from F. Chapoton, Jan 01 2022 STATUS approved

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Last modified September 24 19:02 EDT 2023. Contains 365581 sequences. (Running on oeis4.)