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A018932 The number of permutations of n cards in which 4 will be the next hit after 2. 2
0, 3, 10, 60, 408, 3120, 26640, 252000, 2620800, 29756160, 366508800, 4869849600, 69455232000, 1058593536000, 17174123366400, 295534407168000, 5377157001216000, 103149354147840000, 2080771454361600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

From the game of Mousetrap.

LINKS

G. C. Greubel, Table of n, a(n) for n = 4..450

D. J. Mundform, A problem of permutations: the Game of 'Moustrap', Eur. J. Combinat. 15 (1994) 555-560.

FORMULA

a(n) = (n-2)! - 3*(n-3)! + 2*(n-4)! if n > 5. - R. J. Mathar, Oct 02 2008

E.g.f.: (x*(1020 - 1290*x + 340*x^2 - 15*x^3 + 3*x^4) + 60*(17 - 30*x + 15*x^2 - 2*x^3)*log(1-x))/360. - G. C. Greubel, Feb 21 2019

MAPLE

0, 3, seq((n^2-8*n+17)*factorial(n-4), n=6..30); # Muniru A Asiru, Feb 22 2019

MATHEMATICA

Join[{0, 3}, Table[(n^2-8*n+17)*(n-4)!, {n, 6, 30}]] (* G. C. Greubel, Feb 21 2019 *)

PROG

(PARI) for(n=4, 30, print1(if(n==4, 0, if(n==5, 3, (n^2-8*n+17)*(n-4)!)), ", ")) \\ G. C. Greubel, Feb 21 2019

(MAGMA) [0, 3] cat [(n^2-8*n+17)*Factorial(n-4): n in [6..30]]; // G. C. Greubel, Feb 21 2019

(Sage) [0, 3] + [(n^2-8*n+17)*factorial(n-4) for n in (6..30)] # G. C. Greubel, Feb 21 2019

(GAP) Concatenation([0, 3], List([6..30], n-> (n^2-8*n+17)*Factorial(n-4) )) # G. C. Greubel, Feb 21 2019

CROSSREFS

Cf. A002468.

Sequence in context: A158873 A103591 A245312 * A111562 A009654 A013565

Adjacent sequences:  A018929 A018930 A018931 * A018933 A018934 A018935

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Changed offset to 4. More terms, better definition and link from R. J. Mathar, Oct 02 2008

STATUS

approved

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Last modified June 24 02:18 EDT 2021. Contains 345411 sequences. (Running on oeis4.)