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A055789
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a(n) = binomial(n, round(sqrt(n))).
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1
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1, 1, 2, 3, 6, 10, 15, 35, 56, 84, 120, 165, 220, 715, 1001, 1365, 1820, 2380, 3060, 3876, 4845, 20349, 26334, 33649, 42504, 53130, 65780, 80730, 98280, 118755, 142506, 736281, 906192, 1107568, 1344904, 1623160, 1947792, 2324784, 2760681
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(9) = C(9,3) = 9!/(3!*6!) = 84
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MAPLE
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seq( binomial(n, round(sqrt(n))), n=0..40); # G. C. Greubel, Jan 25 2020
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MATHEMATICA
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Table[Binomial[n, Round[Sqrt[n]]], {n, 0, 40}] (* G. C. Greubel, Jan 25 2020 *)
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PROG
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(PARI) vector(40, n, binomial(n, round(sqrt(n))) ) \\ G. C. Greubel, Jan 25 2020
(Magma) [Binomial(n, Round(Sqrt(n))): n in [0..40]]; // G. C. Greubel, Jan 25 2020
(Sage) [binomial(n, round(sqrt(n))) for n in (0..40)] # G. C. Greubel, Jan 25 2020
(Python)
from math import comb, isqrt
def A055789(n): return comb(n, (m:=isqrt(n))+ int((n-m*(m+1)<<2)>=1)) # Chai Wah Wu, Jul 29 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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