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A091599 Triangle read by rows: T(n,k) is the number of nonseparable planar maps with r*n edges and a fixed outer face of r*k edges which are invariant under a rotation of 1/r for any r >= 2 (independent of actual value of r). 3
1, 2, 1, 6, 6, 1, 24, 26, 12, 1, 110, 120, 75, 20, 1, 546, 594, 416, 174, 30, 1, 2856, 3094, 2289, 1176, 350, 42, 1, 15504, 16728, 12768, 7322, 2880, 636, 56, 1, 86526, 93024, 72420, 44388, 20475, 6324, 1071, 72, 1, 493350, 528770, 417240, 267240, 136252, 51495, 12740, 1700, 90, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table I in the Brown reference.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.

FORMULA

T(n, k) = k*(Sum_{j=k..min(n, 2*k)} (2*j-k)*(j-1)!*(3*n-j-k-1)!/(((j-k)!)^2*(2*k-j)!*(n-j)!))/(2*n-k)!

EXAMPLE

Triangle starts:

    1;

    2,   1;

    6,   6,  1;

   24,  26, 12,  1;

  110, 120, 75, 20, 1;

  ...

MAPLE

T := proc(n, k) if k<=n then k*sum((2*j-k)*(j-1)!*(3*n-j-k-1)!/(j-k)!/(j-k)!/(2*k-j)!/(n-j)!, j=k..min(n, 2*k))/(2*n-k)! else 0 fi end: seq(seq(T(n, k), k=1..n), n=1..11);

PROG

(PARI) T(n, k) = k*sum(j=k, min(n, 2*k), (2*j-k)*(j-1)!*(3*n-j-k-1)!/(((j-k)!)^2*(2*k-j)!*(n-j)!))/(2*n-k)!

for(n=1, 10, for(k=1, n, print1(T(n, k), ", ")); print) \\ Andrew Howroyd, Mar 29 2021

CROSSREFS

Column 1 gives A046646, column 2 gives A046647, row sums give A000259.

Same as A046651 but with rows reversed.

Cf. A046653, A091665.

Sequence in context: A244888 A130561 A157400 * A048999 A066667 A105278

Adjacent sequences:  A091596 A091597 A091598 * A091600 A091601 A091602

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Mar 03 2004

EXTENSIONS

Name clarified by Andrew Howroyd, Mar 29 2021

STATUS

approved

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Last modified April 15 23:51 EDT 2021. Contains 343018 sequences. (Running on oeis4.)