OFFSET
0,1
COMMENTS
A combinatorial interpretation for this sequence in terms of a family of plane trees is given in [Schaeffer, Corollary 2 with k = 5].
A combinatorial interpretation for this sequence in terms of a family of four-dimensional stacked spheres is given in [Thorlieffson, Table 3 in Appendix B]. - Robert A. Russell, Mar 15 2012
LINKS
G. Schaeffer, A combinatorial interpretation of super-Catalan numbers of order two (2001).
G. Thorlieffson, P. Bialis, B. Petersson, The weak-coupling limit of simplicial quantum gravity, Nuclear Physics B, Volume 550, Issues 1-2, 14 June 1999, Pages 465-491.
FORMULA
a(n) = 6/((4*n+1)*(4*n+2))*binomial(5*n,n).
D-finite with recurrence 8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Mar 29 2023
MAPLE
A197272 := proc(n)
6/((4*n+1)*(4*n+2))*binomial(5*n, n)
end proc:
seq(A197272(n), n=0..40) ; # R. J. Mathar, Mar 29 2023
MATHEMATICA
Table[6/((4n+1)(4n+2)) Binomial[5n, n], {n, 0, 20}] (* Harvey P. Dale, Aug 08 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Oct 12 2011
STATUS
approved