%I A006858 M4935
%S A006858 0,1,14,84,330,1001,2548,5712,11628,21945,38962,65780,106470,166257,
%T A006858 251720,371008,534072,752913,1041846,1417780,1900514,2513049,3281916,
%U A006858 4237520,5414500,6852105,8594586,10691604,13198654,16177505,19696656
%N A006858 G.f.: x(1+x)(1+6x+x^2)/(1-x)^7.
%C A006858 Arises in enumerating paths in the plane.
%C A006858 a(n+1) is the determinant of the n-by-n Hankel matrix whose first row 
               is the Catalan numbers C_n (A000108) beginning at C_4 = 14. Example 
               (n=3): det[{{14, 42, 132}, {42, 132, 429}, {132, 429, 1430}}] = 330. 
               - David Callan (callan(AT)stat.wisc.edu), Mar 30 2007
%D A006858 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006858 G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected 
               with lattice paths, European J. Combin., 2 (1981), 55-60.
%D A006858 J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 
               201 (2006), 143-179. [Th. 7.2(ii), case a=1]
%D A006858 Stanley, R. P., Enumerative Combinatorics, Volume 1 (1986), p. 221, Example 
               4.5.18.
%H A006858 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A006858 a(n) = (n+1)*binomial(2n+4, 5)/12 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Mar 06 2004
%p A006858 series((x+7*x^2+7*x^3+x^4)/(1-x)^7,x,50);
%p A006858 b:=binomial; t72b:= proc(a,k) ((a+k+1)/(a+1)) * b(k+2*a+1,k)*b(k+3*a/
               2+1,k)/(b(k+a/2,k)); end; [seq(t72b(1,k),k=0..40)];
%Y A006858 Cf. A006332.
%Y A006858 Sequence in context: A107935 A008451 A033276 this_sequence A027818 A054149 
               A025607
%Y A006858 Adjacent sequences: A006855 A006856 A006857 this_sequence A006859 A006860 
               A006861
%K A006858 nonn,easy
%O A006858 0,3
%A A006858 Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
%E A006858 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2007