A347304
a(n) = n!/(floor(n/2)!*floor(n/3)!*floor(n/6)!).
Original entry on oeis.org
1, 1, 2, 6, 12, 60, 60, 420, 840, 2520, 5040, 55440, 13860, 180180, 360360, 1081080, 2162160, 36756720, 4084080, 77597520, 155195040, 465585120, 931170240, 21416915520, 1338557220, 33463930500, 66927861000, 200783583000, 401567166000, 11645447814000, 465817912560
Offset: 0
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a(n) = n!/((n\2)!*(n\3)!*(n\6)!); \\ Seiichi Manyama, Aug 28 2021
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from math import factorial
def A347304(n): return factorial(n)//factorial(n//2)//factorial(n//3)//factorial(n//6) # Chai Wah Wu, Aug 28 2021
A351823
Triangular array read by rows. T(n,k) is the number of sets of lists (as in A000262(n)) with exactly k size 2 lists, n >= 0, 0 <= k <= floor(n/2).
Original entry on oeis.org
1, 1, 1, 2, 7, 6, 49, 12, 12, 301, 140, 60, 2281, 1470, 180, 120, 21211, 12642, 2940, 840, 220417, 127736, 41160, 3360, 1680, 2528569, 1527192, 455112, 70560, 15120, 32014801, 19837530, 5748120, 1234800, 75600, 30240, 442974511, 278142590, 83995560, 16687440, 1940400, 332640
Offset: 0
Triangle T(n,k) begins:
1;
1;
1, 2;
7, 6;
49, 12, 12;
301, 140, 60;
2281, 1470, 180, 120;
21211, 12642, 2940, 840;
...
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b:= proc(n) option remember; expand(`if`(n=0, 1, add(j!*
`if`(j=2, x, 1)*b(n-j)*binomial(n-1, j-1), j=1..n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n/2))(b(n)):
seq(T(n), n=0..12); # Alois P. Heinz, Feb 20 2022
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nn = 7; Map[Select[#, # > 0 &] &,Range[0, nn]! CoefficientList[Series[Exp[ x/(1 - x) - x ^2 + y x^2], {x, 0, nn}], {x, y}]] // Grid
A374647
a(n) = n! / floor(2n/3)!.
Original entry on oeis.org
1, 1, 2, 3, 12, 20, 30, 210, 336, 504, 5040, 7920, 11880, 154440, 240240, 360360, 5765760, 8910720, 13366080, 253955520, 390700800, 586051200, 12893126400, 19769460480, 29654190720, 741354768000, 1133836704000, 1700755056000, 47621141568000, 72684900288000
Offset: 0
A374648
a(n) = n! / (floor(n/3))! - n! / (floor(n/2))!.
Original entry on oeis.org
0, 0, 0, 0, 12, 60, 240, 1680, 18480, 45360, 574560, 6320160, 19293120, 250810560, 3615131520, 10637827200, 173837664000, 2955240288000, 8874542476800, 168616307059200, 3378360124339200, 10123012406707200, 222987858828134400, 5128720753047091200
Offset: 0
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