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 A000426 Coefficients of ménage hit polynomials. (Formerly M4515 N1910) 3
 0, 1, 1, 1, 8, 35, 211, 1459, 11584, 103605, 1030805, 11291237, 135015896, 1749915271, 24435107047, 365696282855, 5839492221440, 99096354764009, 1780930394412009, 33789956266629001, 674939337282352360, 14157377139256183723 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198. 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). H. M. Taylor, A problem on arrangements, Mess. Math., 32 (1902), 60ff. LINKS David W. Wilson, Table of n, a(n) for n = 1..100 R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976 H. M. Taylor, A problem on arrangements, Mess. Math., 32 (1902), 60ff. [Annotated scanned copy] FORMULA a(n) = SUM(k = 2..n, ((-1)^k (2n-k-1)! (n-k)!)/((2n-2k)! (k-2)!)) a(n) = A000033(n)/n. a(n) = ((2*n-5)*a(n-1) + (5*n-11)*a(n-2) + (5*n-14)*a(n-3) + (2*n-5)*a(n-4) + 2*a(n-5))/2 for n >= 6. Shorter recurrence: (14*n-67)*a(n) = (14*n^2-95*n+137)*a(n-1) + (14*n^2-105*n+180)*a(n-2) - 24*a(n-4)+(57-10*n)*a(n-3). - Vaclav Kotesovec, Oct 26 2012 a(n) ~ 2/e^2*(n-1)!. - Vaclav Kotesovec, Oct 26 2012 MATHEMATICA Table[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 *) CROSSREFS Cf. A000179, A000271. A diagonal of A058057. Sequence in context: A263520 A223901 A192257 * A250889 A200312 A089698 Adjacent sequences:  A000423 A000424 A000425 * A000427 A000428 A000429 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by David W. Wilson, Dec 27 2007 STATUS approved

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