|
Search: id:A069271
|
|
| |
|
| 1, 2, 9, 52, 340, 2394, 17710, 135720, 1068012, 8579560, 70068713, 580034052, 4855986044, 41043559340, 349756577100, 3001701610320, 25921837477692, 225083787458904, 1963988670706228, 17211860478150800, 151433425446423120
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Bacher: "We describe the statistics of checkerboard triangulations obtained by coloring black every other triangle in triangulations of convex polygons." A069271 occurs on p. 12 as the second of two "extremal sequences" (the first being A002293) of an array of coefficients of polynomials, whose generating functions are given in terms of hypergeometric fnctions. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 05 2007
|
|
LINKS
|
J.-C. Novelli and J.-Y. Thibon, Noncommutative Symmetric Functions and Lagrange Inversion
Roland Bacher, Fair Triangulations
|
|
FORMULA
|
a(n) =A069270(n+1, n) =A005810(n)*A016813(n)/A060544(n+1)
|
|
EXAMPLE
|
a(3)=C(4*3+1,3)*2/(3*3+2)=C(13,3)*2/11=286*2/11=52.
|
|
MAPLE
|
BB:=[T, {T=Prod(Z, Z, Z, F, F), F=Sequence(B), B=Prod(F, F, F, Z)}, unlabeled]: seq(count(BB, size=i), i=3..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2007
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x/(1+x^2)^2+O(x^(2*n+2))), 2*n+1)) (from R. Stephan)
|
|
CROSSREFS
|
Cf. A002293, A006013, A006632, A069270 for similar generalized Catalan sequences.
Cf. A002293.
Sequence in context: A009310 A091319 A003584 this_sequence A006152 A143508 A052882
Adjacent sequences: A069268 A069269 A069270 this_sequence A069272 A069273 A069274
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), Mar 12 2002
|
|
|
Search completed in 0.002 seconds
|
