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!)
 A006902 a(n) = (2n)! * Sum_{k=0..n} (-1)^k * binomial(n,k) / (n+k)!. (Formerly M4003) 36
 1, 1, 5, 47, 641, 11389, 248749, 6439075, 192621953, 6536413529, 248040482741, 10407123510871, 478360626529345, 23903857657114837, 1290205338991689821, 74803882225482661259, 4636427218380366565889, 305927317398343461908785, 21410426012751471702223333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of words on {1,1,2,2,...,n,n} with longest increasing subsequence of length n. a(2) = 5: 1122, 1212, 1221, 2112, 2121. - Alois P. Heinz, Jan 18 2016 REFERENCES J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congress. Numerantium, 33 (1981), 75-80. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..360 (terms n = 1..100 from T. D. Noe) FORMULA a(n) = n!*LaguerreL(n, n, 1). - Vladeta Jovovic, May 11 2003 (n-2)*a(n)-(n^3+n^2-7*n+4)*a(n-1)+2*(2*n-3)*(n-1)^3*a(n-2) = 0. - Vladeta Jovovic, Jul 16 2004 a(n) ~ n^n*2^(2*n+1/2)/exp(n+1). - Vaclav Kotesovec, Jun 22 2013 a(n) = B_n(n*0!,(n-1)*1!,...,1*(n-1)!), where B_n(x1,...,xn) is the n-th complete Bell polynomial. - Max Alekseyev, Jul 04 2015 a(n) = n!*binomial(2*n,n)*hypergeom([-n], [n+1], 1). - Peter Luschny, May 04 2017 a(n) = n!*Z(S_n; n, n-1, ..., 1) where Z(S_n) is the cycle index of the symmetric group of order n. - Sean A. Irvine, Nov 14 2017 a(n) = n! * [x^n] exp(-x/(1 - x))/(1 - x)^(n+1). - Ilya Gutkovskiy, Nov 21 2017 MAPLE a:= proc(n) option remember; `if`(n<3, [1\$2, 5][n+1], (       (n^3+n^2-7*n+4)*a(n-1)-2*(2*n-3)*(n-1)^3*a(n-2))/(n-2))     end: seq(a(n), n=0..20);  # Alois P. Heinz, Jan 15 2016 MATHEMATICA Table[(-1)^k HypergeometricU[-k, 1 + k, 1], {k, 1, 10}] (* Vladimir Reshetnikov, Feb 16 2011 *) PROG (PARI) a(n)=round(hyperu(-n, n+1, 1)*(-1)^n) \\ Charles R Greathouse IV, Dec 30 2014 CROSSREFS Row n=2 of A047909. Main diagonal of A267480. Cf. A082545. Sequence in context: A074192 A058806 A302616 * A180254 A127696 A088691 Adjacent sequences:  A006899 A006900 A006901 * A006903 A006904 A006905 KEYWORD nonn,easy AUTHOR EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Jan 15 2016 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 30 08:04 EDT 2020. Contains 334712 sequences. (Running on oeis4.)