A373134 Expansion of e.g.f. (1/2)*(x^2*exp(x))*(sinh(x))^2.
0, 0, 0, 0, 12, 60, 300, 1260, 5096, 19656, 73800, 270600, 974292, 3454308, 12090260, 41850900, 143489040, 487862736, 1646537040, 5520741840, 18402473180, 61018726860, 201361799100, 661617339900, 2165293112952, 7060738411800, 22947399839000, 74349575478360, 240206320776996, 773998144725876
Offset: 0
Keywords
Examples
For n = 6, we have the following cases:
{1}, {2}, {(3), (4), 5, 6} (90 of these),
{2}, {1}, {(3), (4), 5, 6} (90 of these),
{1, 2, 3}, {4}, {(5), (6)} (60 of these),
{1}, {2, 3, 4}, {(5), (6)} (60 of these),
where the two elements selected from the third set are in parentheses.
Formula
a(n) = binomial(n,2)*(3^(n-2) + (-1)^n - 2)/4.
Comments