A001568 Related to 3-line Latin rectangles.

1, -1, -1, 2, 49, 629, 6961, 38366, -1899687, -133065253, -6482111309, -281940658286, -10702380933551, -247708227641863, 14512103549430397, 3377044611825908414, 433180638973276282801, 47474992085447610990231

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• more

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]
• Index entries for sequences related to Latin squares and rectangles

Programs

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

Extensions

Signs added by N. J. A. Sloane, Jul 23 2015

More terms from F. Chapoton, Jan 01 2022