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A261398
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Integer coefficients arising from a formula for Sum_{m>=1} sin(Pi*m/3)^2/m^2.
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2
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1, 2, 6, 32, 230, 2112, 23548, 309248, 4675014, 79969280, 1527092468, 32203259904, 743288515164, 18638209056768, 504541774904760, 14664951970922496, 455522635895576646, 15058911973677465600, 527896878148304296900, 19559986314930028544000, 763820398700983273655796, 31353195811771939838492672
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{i=0..floor((n-1)/2)} (-1)^i*binomial(n,i)*(n-2*i)^(n-1).
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MAPLE
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add( (-1)^i*binomial(n, i)*(n-2*i)^(n-1), i=0..floor((n-1)/2)) ;
end proc:
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MATHEMATICA
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Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}], {n, 1, 20}] (* Vladimir Reshetnikov, Sep 05 2016 *)
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PROG
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(PARI) a(n) = sum(i=0, (n-1)\2, (-1)^i*binomial(n, i)*(n-2*i)^(n-1)); \\ Michel Marcus, Sep 05 2016
(Magma) [(&+[(-1)^j*Binomial(n, j)*(n-2*j)^(n-1): j in [0..Floor(n/2)]]): n in [1..25]]; // G. C. Greubel, Apr 01 2022
(Sage) [sum((-1)^j*binomial(n, j)*(n-2*j)^(n-1) for j in (0..(n//2))) for n in (1..25)] # G. C. Greubel, Apr 01 2022
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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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