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%I #10 Dec 10 2023 17:42:16
%S 1,2,1520,134640,24272640,7527582720,3517707916800,2320039459584000,
%T 2047894341292800000,2331675471496250880000,3325719719034680647680000,
%U 5807364536076078278983680000,12184314075622103163420672000000
%N a(1)=1, a(2)=2; thereafter a(n) = (1/n!)*Sum_{i=0..floor(n/2)} 4*(2*n+1)!*(2*n-i-4)!/(i!*(n-i-2)!*(2*n-i+1)).
%C Related to the enumeration of rooted simple planar maps with n edges.
%C See A329776 for another version. Presumably only one of the two versions is correct.
%D Liu, Yanpei, On the enumeration of simple planar maps, RUTCOR Research Report #37-87, Nov. 1987, RUTCOR, Hill Center, Rutgers University, NJ. See (20).
%D Liu, Yanpei, An enumerating equation of simple planar maps with face partition, RUTCOR Research Report #38-87, Nov. 1987, RUTCOR, Hill Center, Rutgers University, NJ. See (22).
%H Yanpei Liu, <a href="https://doi.org/10.1016/0012-365X(93)90009-I">On functional equations arising from map enumerations</a>, Discrete Mathematics 123.1-3 (1993): 93-109. See (4.16).
%p f2:=n -> (1/n!)*add(4*(2*n+1)!*(2*n-i-4)!/(i!*(n-i-2)!*(2*n-i+1)),i=0..floor(n/2));
%p [1, 2, seq(f2(m), m=3..10)];
%Y Cf. A329776.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 25 2019
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