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!)
 A061206 a(n) = total number of occurrences of the consecutive pattern 1324 in all permutations of [n+3]. 12
 1, 10, 90, 840, 8400, 90720, 1058400, 13305600, 179625600, 2594592000, 39956716800, 653837184000, 11333177856000, 207484333056000, 4001483566080000, 81096733605888000, 1723305589125120000, 38318206628782080000, 889833909490606080000, 21543347282404147200000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of sequences of n+3 balls colored with at most n colors such that exactly four balls are the same color as some other ball in the sequence. - Jeremy Dover, Sep 27 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..300 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets FORMULA a(n) = n*(n+3)!/24. If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i) * x^(k-j), then a(n-3) = (-1)^n*f(n,4,-2), (n >= 4). - Milan Janjic, Mar 01 2009 E.g.f.: x/(1-x)^5. (This was initiated by e-mail exchange with Gary Detlefs.) - Wolfdieter Lang, May 28 2010 a(n) = ((n+4)!/6) * Sum_{k=1..n} (k+2)!/(k+4)!. - Gary Detlefs, Aug 05 2010 a(n) = Sum_{k>0} k * A264173(n+3,k). - Alois P. Heinz, Nov 06 2015 a(n) = n!*binomial(-n,4). - Peter Luschny, Apr 29 2016 EXAMPLE a(4)=840 because 4*(7!)/24 = 4*7*6*5 = 840. MAPLE a := n -> n!*binomial(-n, 4): seq(a(n), n=1..20); # Peter Luschny, Apr 29 2016 MATHEMATICA Array[# (# + 3)!/24 &, 20] (* or *) Array[#!*Binomial[-#, 4] &, 20] (* Michael De Vlieger, Sep 30 2017 *) PROG (Sage) [binomial(n, 4)*factorial (n-3) for n in range(4, 21)] # Zerinvary Lajos, Jul 07 2009 (MAGMA) [n*Factorial(n+3)/24: n in [1..20]]; // Vincenzo Librandi, Oct 11 2011 (PARI) a(n) = n*(n+3)!/24; \\ Altug Alkan, Oct 08 2017 CROSSREFS Cf. A000142, A001286, A001339, A001563, A005990, A264173. Sequence in context: A003952 A252703 A033136 * A199527 A137684 A097394 Adjacent sequences:  A061203 A061204 A061205 * A061207 A061208 A061209 KEYWORD nonn AUTHOR Melvin J. Knight (knightmj(AT)juno.com), May 30 2001 EXTENSIONS More terms from Jason Earls, Jun 12 2001 Corrected by Zerinvary Lajos, Jul 07 2009 More precise definition from Alois P. Heinz, Nov 06 2015 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 June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)