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A098276 Difference between the number of even reduced Latin rectangles of size 3 X n and the number of odd ones. 1
1, 0, 2, 0, 72, -320, 3600, -32256, 344960, -3926016, 48625920, -648243200, 9270125568, -141579509760, 2300668418048, -39642283376640, 722055883161600, -13863472939925504, 279868860012625920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

J. Zeng, The generating function for the difference in even and odd three-line latin rectangles, Ann. Sci. Math. Quebec 20/1 (1996) 105-108. [alternate link]

FORMULA

E.g.f.: x + [(1-x)^2/(1+x)+x/(1+x)^2] * exp(2x). - corrected by Vaclav Kotesovec, Sep 29 2013

a(n) ~ n! * (-1)^(n+1) * n * exp(-2). - Vaclav Kotesovec, Sep 29 2013

MATHEMATICA

Rest[CoefficientList[Series[x + ((1-x)^2/(1+x)+x/(1+x)^2)*E^(2*x), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 29 2013 *)

PROG

(PARI) a(n)=polcoeff(serlaplace(exp(2*x)*((1-x)^2/(1+x)+x/(1+x)^2)), n)

(PARI) a(n)=(-1)^(n-1)*(n-2)*n!/2*polcoeff(Ser(exp(2*(atanh(x)-x))), n)

CROSSREFS

Cf. A000186.

Sequence in context: A264437 A306061 A195209 * A215880 A030129 A012647

Adjacent sequences:  A098273 A098274 A098275 * A098277 A098278 A098279

KEYWORD

sign,easy

AUTHOR

Ralf Stephan, Sep 06 2004

STATUS

approved

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Last modified August 20 06:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)