The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006013 a(n) = binomial(3*n+1,n)/(n+1). (Formerly M1782) 81
 1, 2, 7, 30, 143, 728, 3876, 21318, 120175, 690690, 4032015, 23841480, 142498692, 859515920, 5225264024, 31983672534, 196947587823, 1219199353190, 7583142491925, 47365474641870, 296983176369495, 1868545312633440, 11793499763070480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Enumerates pairs of ternary trees [Knuth, 2014]. - N. J. A. Sloane, Dec 09 2014 G.f. (offset 1) is series reversion of x - 2x^2 + x^3. Hankel transform is A005156(n+1). - Paul Barry, Jan 20 2007 a(n) = number of ways to connect 2n-2 points labeled 1,2,...,2n-2 in a line with 0 or more noncrossing arcs above the line such that each maximal contiguous sequence of isolated points has even length. For example, with arcs separated by dashes, a(3)=7 counts {} (no arcs), 12, 14, 23, 34, 12-34, 14-23. It does not count 13 because 2 is an isolated point. - David Callan, Sep 18 2007 In my 2003 paper I introduced L-algebras. These are K-vector spaces equipped with two binary operations > and < satisfying (x>y)(y0. - Bruno Berselli, Jan 20 2014 From Ilya Gutkovskiy, Dec 29 2016: (Start) E.g.f.: 2F2(2/3,4/3; 3/2,2; 27*x/4). a(n) ~ 3^(3*n+3/2)/(sqrt(Pi)*4^(n+1)*n^(3/2)). (End) EXAMPLE a(3) = 30 since the top row of Q^3 = (12, 12, 5, 1). MAPLE BB:=[T, {T=Prod(Z, Z, F, F), F=Sequence(B), B=Prod(F, F, Z)}, unlabeled]: seq(count(BB, size=i), i=2..24); # Zerinvary Lajos, Apr 22 2007 MATHEMATICA InverseSeries[Series[y-2*y^2+y^3, {y, 0, 32}], x] Binomial[3#+1, #]/(#+1)&/@Range[0, 30]  (* Harvey P. Dale, Mar 16 2011 *) PROG (PARI) a(n)=if(n<0, 0, (3*n+1)!/(n+1)!/(2*n+1)!) (PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x-2*x^2+x^3+x^2*O(x^n)), n+1)) (Sage) def A006013_list(n) :     D = *(n+1); D = 1     R = []; b = false; h = 1     for i in range(2*n) :         for k in (1..h) : D[k] += D[k-1]         if b : R.append(D[h]); h += 1         b = not b     return R A006013_list(23) # Peter Luschny, May 03 2012 (MAGMA) [Binomial(3*n+1, n)/(n+1): n in [0..30]]; // Vincenzo Librandi, Mar 29 2015 (Haskell) a006013 n = a007318 (3 * n + 1) n `div` (n + 1) a006013' n = a258708 (2 * n + 1) n -- Reinhard Zumkeller, Jun 22 2015 CROSSREFS These are the odd indices of A047749. Cf. A121645, A115728, A143603, A236194. Cf. A007318, A071948, A110616, A258708. Sequence in context: A260773 A174796 A046648 * A187979 A243632 A196148 Adjacent sequences:  A006010 A006011 A006012 * A006014 A006015 A006016 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Feb 21 2008 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 January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)