OFFSET
0,4
COMMENTS
These are also called [n,0]-triangulations.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.
W. G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. [Annotated scanned copy]
C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)
MAPLE
Dc := proc(n, m) 2*(2*m+3)!*(4*n+2*m+1)!/m!/(m+2)!/n!/(3*n+2*m+3)! ; end:
A000260 := proc(n) Dc(n, 0) ; end:
Dx2 := proc(nmax) add( A000260(n)*x^(2*n), n=0..nmax) ; end:
o := 20: Order := 2*o-1 : j := solve( J0=1+x*J0+x^2*J0*(1+x*J0/2)*series(J0^2-Dx2(o), x=0, 2*o-1), J0) ;
for n from 0 to 2*o-2 do printf("%d, ", coeftayl(j, x=0, n)) ; od: # R. J. Mathar, Oct 29 2008
MATHEMATICA
seq[m_] := Module[{q}, q = Sum[x^(2n) Binomial[4n+2, n+1]/ ((2n+1)(3n+2)), {n, 0, Quotient[m, 2]}]; p = 1+O[x]; Do[p = 1 + x*p + x^2*p*(1+x*p/2)(p^2-q), {n, 1, m}]; CoefficientList[p, x]];
seq[30] (* Jean-François Alcover, Apr 25 2023, after Andrew Howroyd *)
PROG
(PARI) seq(n)={my(q=sum(n=0, n\2, x^(2*n)*binomial(4*n+2, n+1)/((2*n+1)*(3*n+2))), p=1+O(x)); for(n=1, n, p = 1 + x*p + x^2*p*(1 + x*p/2)*(p^2 - q)); Vec(p)} \\ Andrew Howroyd, Feb 24 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, Oct 29 2008
Name clarified and terms a(27) and beyond from Andrew Howroyd, Feb 24 2021
STATUS
approved