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%I #15 Nov 03 2021 11:38:03
%S 2,6,30,182,1224,8778,65780,508950,4034712,32602328,267535086,
%T 2223463866,18676869400,158310871740,1352392098120,11631593739990,
%U 100637721972216,875325840117960,7649219033276888,67126255864788120,591311470790795040,5226783343136641530
%N a(n) = 6*binomial(4*n-1,n-1)/(4*n-1).
%D Madeline Jones, The Mysterious Flexagons (1966).
%D M. Kosters, A theory of hexaflexagons, Nieuw Archief Wisk., 17 (1999), 349-362.
%H Vernon Gutenkunst, <a href="http://members.aol.com/verndrei/flexh01.html">Trailblazing Hexagons</a>
%H C. O. Oakley, and R. J. Wisner, <a href="https://doi.org/10.2307/2310544">Flexagons</a>, Am. Math. Monthly 64 (3) (1957) 143-154, U_{3*lambda}.
%F D-finite with recurrence 3*n*(3*n-1)*(3*n-2)*a(n) -8*(4*n-5)*(4*n-3)*(2*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 05 2021
%t Table[c=4n-1;6 Binomial[c,n-1]/c,{n,25}] (* _Harvey P. Dale_, Sep 13 2011 *)
%Y Equals 2*A006632.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 05 2005