The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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, 311135096550816014651 (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 a(n) = round((exp(-2)*(8*BesselK(n,2) - (4*n-10)*BesselK(n-1,2)))) for n > 6. - Mark van Hoeij, Jun 09 2019 a(n)+2*a(n+p)+a(n+2*p) is divisible by p for any prime p. - Mark van Hoeij, Jun 13 2019 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 *) PROG (Magma) [0] cat [&+[(-1)^k*Factorial(2*n-k-1)*Factorial(n-k) / (Factorial(2*n-2*k)*Factorial(k-2)): k in [2..n]]: n in [2..25]]; // Vincenzo Librandi, Jun 11 2019 CROSSREFS Cf. A000179, A000271. A diagonal of A058057. Sequence in context: A223901 A192257 A297609 * A250889 A200312 A339325 Adjacent sequences: A000423 A000424 A000425 * A000427 A000428 A000429 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by David W. Wilson, Dec 27 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 31 15:31 EDT 2023. Contains 361668 sequences. (Running on oeis4.)