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A371372
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a(n) = Sum_{d|2*n} binomial(4*n/d-1, 2*n/d)*phi(d))/(4*n) for n>0 with a(0)=0.
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1
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0, 1, 5, 40, 405, 4626, 56360, 716430, 9392085, 126044248, 1723083930, 23910223514, 335912566824, 4768447532200, 68291880722182, 985538181002940, 14317376105810133, 209213540276280758, 3073003751985537656, 45346188478477675122, 671920054584212646330, 9993514798883508502188
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of subsets of {1, 2, ..., 4*n-1} of size 2*n that sum to 3*n mod 4*n [Donderwinkel/Kolesnik].
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LINKS
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MATHEMATICA
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Join[{0}, Table[Sum[Binomial[4*n/d - 1, 2*n/d] * EulerPhi[d] / (4*n), {d, Divisors[2*n]}], {n, 1, 20}]] (* Vaclav Kotesovec, Mar 20 2024 *)
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PROG
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(PARI) a(n) = if (n==0, 0, sumdiv(2*n, d, binomial(4*n/d-1, 2*n/d)*eulerphi(d))/(4*n));
(Python)
from math import comb
from sympy import totient, divisors
def A371372(n): return sum(comb((d<<1)-1, d)*totient((n<<1)//d) for d in divisors(n<<1, generator=True))//n>>2 if n else 0 # Chai Wah Wu, Mar 20 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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