The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A146305 Array T(n,m) = 2*(2m+3)!*(4n+2m+1)!/(m!*(m+2)!*n!*(3n+2m+3)!) read by antidiagonals. 9
 1, 1, 2, 3, 5, 5, 13, 20, 21, 14, 68, 100, 105, 84, 42, 399, 570, 595, 504, 330, 132, 2530, 3542, 3675, 3192, 2310, 1287, 429, 16965, 23400, 24150, 21252, 16170, 10296, 5005, 1430, 118668, 161820, 166257, 147420, 115500, 78936, 45045, 19448, 4862, 857956 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n,m) is the number of rooted nonseparable (2-connected) triangulations of the disk with n internal nodes and 3 + m nodes on the external face. The triangulation has 2*n + m + 1 triangles and 3*(n+1) + 2*m edges. - Andrew Howroyd, Feb 21 2021 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1325 Alin Bostan, Frédéric Chyzak, and Vincent Pilaud, Refined product formulas for Tamari intervals, arXiv:2303.10986 [math.CO], 2023. William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. EXAMPLE The array starts at row n=0 and column m=0 as .....1......2.......5......14.......42.......132 .....1......5......21......84......330......1287 .....3.....20.....105.....504.....2310.....10296 ....13....100.....595....3192....16170.....78936 ....68....570....3675...21252...115500....602316 ...399...3542...24150..147420...844074...4628052 ..2530..23400..166257.1057224..6301680..35939904 .16965.161820.1186680.7791168.47948670.282285432 MAPLE A146305 := proc(n, m) 2*(2*m+3)!*(4*n+2*m+1)!/m!/(m+2)!/n!/(3*n+2*m+3)! ; end proc: for d from 0 to 13 do for m from 0 to d do printf("%d, ", A146305(d-m, m)) ; end do: end do: MATHEMATICA T[n_, m_] := 2*(2*m+3)!*(4*n+2*m+1)!/m!/(m+2)!/n!/(3*n+2*m+3)!; Table[T[n-m, m], {n, 0, 13}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jan 06 2014, after Maple *) PROG (PARI) T(n, m)={2*(2*m+3)!*(4*n+2*m+1)!/(m!*(m+2)!*n!*(3*n+2*m+3)!)} \\ Andrew Howroyd, Feb 21 2021 CROSSREFS Columns m=0..3 are A000260, A197271(n+1), A341853, A341854. Rows n=0..2 are A000108(n+1), A002054(n+1) and A000917. Antidiagonal sums are A000260(n+1). Cf. A169808 (unrooted), A169809 (achiral), A262586 (oriented). Sequence in context: A319631 A097453 A079125 * A342437 A079022 A368706 Adjacent sequences: A146302 A146303 A146304 * A146306 A146307 A146308 KEYWORD easy,nonn,tabl AUTHOR R. J. Mathar, Oct 29 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)