A006430 Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses. (Formerly M4036)

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

1,2

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).

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.

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 *)

Prog

(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

Crossrefs

Column 5 of A342985.

Sequence in context: A006108 A061456 A218994 * A301613 A180766 A007667

Adjacent sequences: A006427 A006428 A006429 * A006431 A006432 A006433

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Title improved by Sean A. Irvine, Apr 10 2017

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

Status

approved