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A324466
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Exponent of highest power of 2 that divides multinomial(3*n;n,n,n).
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2
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0, 1, 1, 4, 1, 2, 4, 6, 1, 2, 2, 7, 4, 5, 6, 8, 1, 2, 2, 5, 2, 3, 7, 9, 4, 5, 5, 9, 6, 7, 8, 10, 1, 2, 2, 5, 2, 3, 5, 7, 2, 3, 3, 10, 7, 8, 9, 11, 4, 5, 5, 8, 5, 6, 9, 11, 6, 7, 7, 11, 8, 9, 10, 12, 1, 2, 2, 5, 2, 3, 5, 7, 2, 3, 3, 8, 5, 6, 7, 9, 2, 3, 3, 6, 3, 4, 10, 12, 7, 8, 8
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OFFSET
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0,4
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LINKS
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FORMULA
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MAPLE
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[seq(padic[ordp](combinat:-multinomial(3*n, n, n, n), 2), n=0..128)];
# alternative:
f:= proc(n) local r, t;
t:= 0; r:= 3*n;
while r > 1 do t:= t + floor(r) - 3*floor(r/3); r:= r/2; od;
t
end proc:
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MATHEMATICA
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Table[IntegerExponent[(3 n)!/n!^3, 2], {n, 0, 100}] (* Vincenzo Librandi Mar 10 2019 *)
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PROG
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(PARI) a(n) = valuation((3*n)!/n!^3, 2); \\ Michel Marcus, Mar 04 2019
(Magma) [Valuation(Factorial(3*n)/Factorial(n)^3, 2): n in [0..100]]; // Vincenzo Librandi, Mar 10 2019
(Python)
from math import factorial
def A324466(n): return (~(m:=factorial(3*n)//factorial(n)**3)& m-1).bit_length() # Chai Wah Wu, Jul 07 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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