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Number of rooted planar maps with 4 vertices and n faces and no isthmuses.
(Formerly M5211)
2

%I M5211 #17 Apr 02 2021 19:54:53

%S 1,30,449,4795,41850,319320,2213665,14283280,87169790,508887860,

%T 2865204762,15654301865,83388235348,434685964540,2223970137825,

%U 11194499812388,55546566721430,272142754971892,1318317357277470,6321681903231990,30037740651227756,141545610360126400

%N Number of rooted planar maps with 4 vertices and n faces and no isthmuses.

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

%H Andrew Howroyd, <a href="/A006421/b006421.txt">Table of n, a(n) for n = 2..500</a>

%H T. R. S. Walsh, A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

%F G.f.: x^2*(1 + 9*g - 9*g^2 - 20*g^3 + 20*g^4)/((1 - g)^5*(1 - 2*g)^8)) where g/x is the g.f. of A000108. - _Andrew Howroyd_, Apr 02 2021

%o (PARI) seq(n)={my(g=x*(1-sqrt(1-4*x + O(x^n)))/(2*x)); Vec((1 + 9*g - 9*g^2 - 20*g^3 + 20*g^4)/((1 - g)^5*(1 - 2*g)^8))} \\ _Andrew Howroyd_, Apr 02 2021

%Y A diagonal of A342981.

%K nonn

%O 2,2

%A _N. J. A. Sloane_

%E a(13) and title improved by _Sean A. Irvine_, Apr 06 2017

%E Terms a(14) and beyond from _Andrew Howroyd_, Apr 02 2021