A000473 Number of genus 0 rooted maps with 5 faces and n vertices. (Formerly M4953 N2122)

14, 386, 5868, 65954, 614404, 5030004, 37460376, 259477218, 1697186964, 10596579708, 63663115880, 370293754740, 2095108370600, 11574690111400, 62629794691632, 332742342741090, 1739371969822260, 8961709528660140, 45576855706440520, 229087231033907708

Offset

4,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.

Links

Andrew Howroyd, Table of n, a(n) for n = 4..500

W. T. Tutte, On the enumeration of planar maps, Bull. Amer. Math. Soc. 74 1968 64-74.

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.

Notes

Formula

G.f.: x^3*(1-sqrt(1-4*x))*(17+16*x-(10+4*x)*sqrt(1-4*x))/(1-4*x)^(11/2). - Sean A. Irvine, Nov 14 2010

Mathematica

CoefficientList[(1/x)(1-Sqrt[1-4x])(17+16x-(10+4x)Sqrt[1-4x])/(1-4x)^(11/2) + O[x]^36, x] (* Jean-François Alcover, Feb 08 2016 *)

Prog

(PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(17+16*x-(10+4*x)*g)/((1-4*x)^5*g))} \\ Andrew Howroyd, Mar 28 2021

Crossrefs

Column 5 of A269920.

Column 0 of A270409.

Sequence in context: A159535 A171718 A270409 * A233094 A211421 A097310

Adjacent sequences: A000470 A000471 A000472 * A000474 A000475 A000476

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved