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A373065
Expansion of e.g.f. (1/2)*(x^2*exp(x))*(cosh(x))^2.
1
0, 0, 1, 3, 18, 70, 315, 1281, 5124, 19692, 73845, 270655, 974358, 3454386, 12090351, 41851005, 143489160, 487862872, 1646537193, 5520742011, 18402473370, 61018727070, 201361799331, 661617340153, 2165293113228, 7060738412100, 22947399839325, 74349575478711, 240206320777374, 773998144726282
OFFSET
0,4
COMMENTS
a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets have an even number of elements, and two elements are selected from the third. "Ordered set partitions", because {}, {1,2}, {(3), (4), 5} is considered to be different from {1,2}, {}, {(3), (4), 5} .
FORMULA
a(n) = binomial(n,2)*(3^(n-2) + (-1)^n + 2)/4.
EXAMPLE
For n = 5, we have the following cases (allowing empty sets):
{}, {1,2}, {(3), (4), 5} (30 of these),
{1,2}, {}, {(3), (4), 5} (30 of these),
{}, {}, {(1), (2), 3, 4, 5} (10 of these),
where the two elements selected from the third set are in parentheses.
CROSSREFS
Cf. A360023.
Sequence in context: A107583 A373651 A157535 * A374487 A098522 A174764
KEYWORD
nonn
AUTHOR
Enrique Navarrete, May 21 2024
STATUS
approved