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A006420
Number of rooted planar maps with 3 vertices and n faces and no isthmuses.
(Formerly M5012)
2
1, 16, 150, 1104, 7077, 41504, 228810, 1205520, 6135690, 30391520, 147277676, 700990752, 3286733805, 15215673408, 69675615234, 316058238864, 1421891923038, 6350464644960, 28179908990772, 124327908683616, 545691921346146, 2383936774151616, 10370479696102500
OFFSET
2,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
FORMULA
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.
PROG
(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
CROSSREFS
A diagonal of A342981.
Sequence in context: A135458 A000486 A223069 * A221422 A049351 A240424
KEYWORD
nonn
EXTENSIONS
a(14) and a(15) from Sean A. Irvine, Apr 05 2017
Terms a(16) and beyond from Andrew Howroyd, Apr 02 2021
STATUS
approved