A006418 Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.

1, 38, 469, 3008, 12843, 42602, 119042, 293578, 658021, 1367170, 2670203, 4953136, 8794967, 15040494, 24893192, 40031954, 62755945, 96162286, 144361777, 212738384, 308258755, 439838594, 618773310, 859240970, 1178886221, 1599494506, 2147766583, 2856204064

Offset: 2

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 = 2..1000
• T. R. S. Walsh, 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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Crossrefs

Column k=5 of A342980.

Programs

PARI

a(n)={if(n<2, 0, (2*n^9 + 81*n^8 + 918*n^7 + 2142*n^6 - 11886*n^5 - 42651*n^4 + 65182*n^3 + 282348*n^2 - 114696*n - 604800)/30240)} \\ Andrew Howroyd, Apr 01 2021

Formula

G.f.: x^2 * (14*x^9 -120*x^8 +440*x^7 -879*x^6 +980*x^5 -482*x^4 -92*x^3 +134*x^2 +28*x+1) / (x-1)^10. - Colin Barker, Apr 09 2013

Extensions

Name clarified and terms a(13) and beyond from Andrew Howroyd, Apr 01 2021