A360023
Expansion of e.g.f. x*exp(x)*(cosh(x))^2.
Original entry on oeis.org
0, 1, 2, 9, 28, 105, 366, 1281, 4376, 14769, 49210, 162393, 531444, 1727193, 5580134, 17936145, 57395632, 182948577, 581130738, 1840247337, 5811307340, 18305618121, 57531942622, 180441092769, 564859072968, 1765184603025, 5507375961386, 17157594341241, 53379182394916, 165856745298489
Offset: 0
For n = 3, the 9 cases are (where the element selected from the third set is in parenthesis):
{}, {}, {(1), 2, 3}
{}, {}, {1, (2), 3}
{}, {}, {1, 2, (3)}
{1,2}, {}, {(3)}
{1,3}, {}, {(2)}
{2,3}, {}, {(1)}
{}, {1,2}, {(3)}
{}, {1,3}, {(2)}
{}, {2,3}, {(1)}.
A360035
Expansion of e.g.f. x*exp(x)*cosh(x)*sinh(x).
Original entry on oeis.org
0, 0, 2, 6, 28, 100, 366, 1274, 4376, 14760, 49210, 162382, 531444, 1727180, 5580134, 17936130, 57395632, 182948560, 581130738, 1840247318, 5811307340, 18305618100, 57531942622, 180441092746, 564859072968, 1765184603000, 5507375961386, 17157594341214, 53379182394916
Offset: 0
For n = 3, the 6 cases are (where the element selected from the third set is in parenthesis):
{}, {1}, {(2), 3}
{}, {1}, {2, (3)}
{}, {2}, {(1), 3}
{}, {2}, {1, (3)}
{}, {3}, {(1), 2}
{}, {3}, {1, (2)}.
A015518 is the case of no element selected in the 3rd set.
A373134
Expansion of e.g.f. (1/2)*(x^2*exp(x))*(sinh(x))^2.
Original entry on oeis.org
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
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.
Showing 1-3 of 3 results.
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