A329775 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)).

1, 2, 1520, 134640, 24272640, 7527582720, 3517707916800, 2320039459584000, 2047894341292800000, 2331675471496250880000, 3325719719034680647680000, 5807364536076078278983680000, 12184314075622103163420672000000

Offset

1,2

Comments

Related to the enumeration of rooted simple planar maps with n edges.

See A329776 for another version. Presumably only one of the two versions is correct.

References

Liu, Yanpei, On the enumeration of simple planar maps, RUTCOR Research Report #37-87, Nov. 1987, RUTCOR, Hill Center, Rutgers University, NJ. See (20).

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).

Links

Table of n, a(n) for n=1..13.

Yanpei Liu, On functional equations arising from map enumerations, Discrete Mathematics 123.1-3 (1993): 93-109. See (4.16).

Maple

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));
[1, 2, seq(f2(m), m=3..10)];

Crossrefs

Cf. A329776.

Sequence in context: A319329 A058423 A233906 * A226699 A110027 A179866

Adjacent sequences: A329772 A329773 A329774 * A329776 A329777 A329778

Keyword

nonn

Author

N. J. A. Sloane, Nov 25 2019

Status

approved