A006430 Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.

0, 5, 360, 7350, 73700, 474588, 2292790, 9046807, 30676440, 92393015, 252872984, 639382605, 1512137536, 3377126024, 7176513960, 14599539314, 28575632350, 54036739617, 99069119952, 176618150000, 306965183268, 521265871700, 866527603370, 1412513294049

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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 = 1..1000
• T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
• Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Crossrefs

Column 5 of A342985.

Programs

Mathematica

A006430[n_] := If[n == 1, 0, (n*(n + 2)*(n + 3)*(n*(n*(n*(n*(n*(n*(n*(n*(n*(23*n + 963) + 17544) + 147952) + 481675) - 1052153) - 7850914) - 2900162) + 60869272) + 37067400) - 179920800))/79833600];
Array[A006430, 50] (* Paolo Xausa, Aug 20 2025 *)

PARI

a(n)={if(n<2, 0, n*(n + 2)*(n + 3)*(23*n^10 + 963*n^9 + 17544*n^8 + 147952*n^7 + 481675*n^6 - 1052153*n^5 - 7850914*n^4 - 2900162*n^3 + 60869272*n^2 + 37067400*n - 179920800)/(2*11!))} \\ Andrew Howroyd, Apr 03 2021

Formula

a(n) = n*(n + 2)*(n + 3)*(23*n^10 + 963*n^9 + 17544*n^8 + 147952*n^7 + 481675*n^6 - 1052153*n^5 - 7850914*n^4 - 2900162*n^3 + 60869272*n^2 + 37067400*n - 179920800)/(2*11!) for n > 1.

Extensions

Title improved by Sean A. Irvine, Apr 10 2017

Terms a(11) and beyond from Andrew Howroyd, Apr 03 2021