A112385 a(n) = 6*binomial(4*n-1,n-1)/(4*n-1).

2, 6, 30, 182, 1224, 8778, 65780, 508950, 4034712, 32602328, 267535086, 2223463866, 18676869400, 158310871740, 1352392098120, 11631593739990, 100637721972216, 875325840117960, 7649219033276888, 67126255864788120, 591311470790795040, 5226783343136641530

Offset: 1

Author

N. J. A. Sloane, Dec 05 2005

Keywords

• nonn
• easy

References

• Madeline Jones, The Mysterious Flexagons (1966).
• M. Kosters, A theory of hexaflexagons, Nieuw Archief Wisk., 17 (1999), 349-362.

Links

• Vernon Gutenkunst, Trailblazing Hexagons
• C. O. Oakley, and R. J. Wisner, Flexagons, Am. Math. Monthly 64 (3) (1957) 143-154, U_{3*lambda}.

Crossrefs

Equals 2*A006632.

Programs

Mathematica

Table[c=4n-1;6 Binomial[c,n-1]/c,{n,25}] (* Harvey P. Dale, Sep 13 2011 *)

Formula

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