A001568 Related to 3-line Latin rectangles. (Formerly M2171 N0867)

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

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

(SageMath)
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 A369943

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