A329776 a(n) = (1/n!)*Sum_{i=0..n-2} 4*(2*n+1)!*(2*n-i-4)!/(i!*(n-i-2)!*(2*n-i+1)).

0, 48, 1520, 134640, 24438960, 7531426560, 3520642164480, 2320166170022400, 2048045044749580800, 2331685226745120153600, 3325737272677280068608000, 5807366064051899816012544000, 12184317992530053651613812480000

Offset

1,2

Comments

For n >= 3, this is related to the enumeration of rooted simple planar maps with n edges.

See A329775 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

f:=m -> (1/m!)*add(4*(2*m+1)!*(2*m-i-4)!/(i!*(m-i-2)!*(2*m-i+1)), i=0..m-2);
[seq(f(m), m=1..40)];

Crossrefs

Cf. A329775.

Sequence in context: A275042 A062195 A264322 * A266160 A004386 A076003

Adjacent sequences: A329773 A329774 A329775 * A329777 A329778 A329779

Keyword

nonn

Author

N. J. A. Sloane, Nov 25 2019

Status

approved