A006418 Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses. (Formerly M5268)

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

2,2

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 = 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).

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

Mathematica

CoefficientList[Series[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, {x, 0, 29}], x] (* Stefano Spezia, Oct 07 2025 *)

Prog

(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

Crossrefs

Column k=5 of A342980.

Sequence in context: A254471 A039685 A389503 * A160317 A088891 A159784

Adjacent sequences: A006415 A006416 A006417 * A006419 A006420 A006421

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved