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A037031
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Number of combinations of n objects taken pi(n) at a time.
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7
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1, 1, 2, 3, 6, 10, 20, 35, 70, 126, 210, 462, 792, 1716, 3003, 5005, 8008, 19448, 31824, 75582, 125970, 203490, 319770, 817190, 1307504, 2042975, 3124550, 4686825, 6906900, 20030010, 30045015, 84672315, 129024480, 193536720, 286097760, 417225900, 600805296
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OFFSET
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0,3
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COMMENTS
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Number of subsets of [n] in which exactly half of the elements are primes: a(6) = 20: {}, {1,2}, {1,3}, {1,5}, {2,4}, {2,6}, {3,4}, {3,6}, {4,5}, {5,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,5}, {1,2,5,6}, {1,3,4,5}, {1,3,5,6}, {2,3,4,6}, {2,4,5,6}, {3,4,5,6}, {1,2,3,4,5,6}. - Alois P. Heinz, Oct 11 2022
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LINKS
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FORMULA
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a(n) = C(n,pi(n)).
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EXAMPLE
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C(16,6) = 8008.
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MAPLE
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MATHEMATICA
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Table[Binomial[n, PrimePi[n]], {n, 40}] (* Harvey P. Dale, Mar 22 2012 *)
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PROG
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(Python)
from math import comb
from sympy import primepi
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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