The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A236921 Number of n-permutations which fix at least one odd prefix. 1
 0, 0, 1, 2, 10, 32, 232, 992, 10096, 53408, 727360, 4569536, 79501696, 578101376, 12337163008, 101945840384, 2582987522560, 23913303638528, 701604503968768, 7194776722623488, 239847438803052544, 2698941227297687552, 100744097104231198720, 1234263151585971974144, 50993324690816940089344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES Warren D. Smith, Postings to Math Fun Mailing List, Feb 06 2014 - Feb 08 2014. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..440 FORMULA a(0)=a(1)=0; a(n) = Sum_(k=1,3,5,..., whichever is odd among {n-1, n-2}) (k!-a(k))*(n-k)!. To see why this recurrence holds, enumerate all the a(n) permutations of {1,2,3,...,n} which fix an odd prefix. They are: perms of form   their count 1...            (n-1)! (123)...        (3!-2)*(n-3)!  where we count only the ones not of the preceding form;  that is, (3!-a(3))*(n-3)! (12345)...      (5!-a(5))*(n-5)! where again count only those not of preceding two forms, and so on. [Warren D. Smith] a(n) ~ (3+(-1)^n)/2 * (n-1)!. - Vaclav Kotesovec, Feb 15 2014 MAPLE F := array(1..66); F[1] := 0; F[2] := 1; for n from  3  to        66  do F[n] := sum( ((2*j+1)! - F[2*j+1]) * (n-(2*j+1))!, j=0 .. (n-2)/2 ); od; # From Warren D. Smith, Feb 12 2014 CROSSREFS Sequence in context: A329427 A004028 A263839 * A316644 A080668 A062453 Adjacent sequences:  A236918 A236919 A236920 * A236922 A236923 A236924 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 11 2014 STATUS approved

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

Last modified May 6 09:25 EDT 2021. Contains 343580 sequences. (Running on oeis4.)