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Number of rooted planar maps with 3 vertices and n faces and no isthmuses.
(Formerly M5012)
2

%I M5012 #19 Apr 06 2021 20:23:50

%S 1,16,150,1104,7077,41504,228810,1205520,6135690,30391520,147277676,

%T 700990752,3286733805,15215673408,69675615234,316058238864,

%U 1421891923038,6350464644960,28179908990772,124327908683616,545691921346146,2383936774151616,10370479696102500

%N Number of rooted planar maps with 3 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="/A006420/b006420.txt">Table of n, a(n) for n = 2..500</a>

%H T. R. S. Walsh and 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 + 2*g - 4*g^2)/((1 - g)^4*(1 - 2*g)^5)) where g/x is the g.f. of A000108.

%o (PARI) seq(n)={my(g=x*(1-sqrt(1-4*x + O(x^n)))/(2*x)); Vec((1 + 2*g - 4*g^2)/((1 - g)^4*(1 - 2*g)^5))} \\ _Andrew Howroyd_, Apr 06 2021

%Y A diagonal of A342981.

%K nonn

%O 2,2

%A _N. J. A. Sloane_

%E a(14) and a(15) from _Sean A. Irvine_, Apr 05 2017

%E Terms a(16) and beyond from _Andrew Howroyd_, Apr 02 2021