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 A000033 Coefficients of ménage hit polynomials. (Formerly M0602 N0216) 6
 0, 2, 3, 4, 40, 210, 1477, 11672, 104256, 1036050, 11338855, 135494844, 1755206648, 24498813794, 366526605705, 5851140525680, 99271367764480, 1783734385752162, 33837677493828171, 675799125332580020, 14173726082929399560, 311462297063636041906 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197. 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 David W. Wilson, Table of n, a(n) for n = 1..100 FORMULA a(n) = coefficient of t^2 in polynomial p(t) = SUM(k = 0..n, (2n C(2n-k,k) (n-k)! (t-1)^k)/(2n-k)) a(n) = SUM(k = 2..n, ((-1)^k n (2n-k-1)! (n-k)!)/((2n-2k)! (k-2)!)) - David W. Wilson, Jun 22 2006 a(n) = n*A000426(n) - Vladeta Jovovic, Dec 27 2007 Recurrence: (n-3)*(n-2)*(2*n-5)*(2*n-7)*a(n) = (n-3)*(n-2)*n*(2*n-7)^2*a(n-1) + (n-4)*(n-3)*n*(2*n-3)^2*a(n-2) + (n-2)*n*(2*n-5)*(2*n-3)*a(n-3). - Vaclav Kotesovec, Oct 26 2012 a(n) ~ 2/e^2*n!. - Vaclav Kotesovec, Oct 26 2012 MATHEMATICA Table[n*Sum[(-1)^k*(2*n-k-1)!*(n-k)!/((2*n-2*k)!*(k-2)!), {k, 2, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 26 2012 *) PROG (Haskell) fac = a000142 a n = sum \$ map f [2..n]   where f k = g k `div` h k         g k = (-1)^k * n * fac (2*n-k-1) * fac (n-k)         h k = fac (2*n-2*k) * fac (k-2) -- James Spahlinger, Oct 08 2012 CROSSREFS A diagonal of A058087. Cf. A000179, A000425. Sequence in context: A037326 A024634 A134305 * A270350 A060411 A037322 Adjacent sequences:  A000030 A000031 A000032 * A000034 A000035 A000036 KEYWORD nonn,easy AUTHOR EXTENSIONS Extended to 34 terms by N. J. A. Sloane, May 25 2005 Edited and further extended by David W. Wilson, Dec 27 2007 STATUS approved

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Last modified October 21 04:12 EDT 2018. Contains 316405 sequences. (Running on oeis4.)