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A261398 Integer coefficients arising from a formula for Sum_{m>=1} sin(Pi*m/3)^2/m^2. 2
1, 2, 6, 32, 230, 2112, 23548, 309248, 4675014, 79969280, 1527092468, 32203259904, 743288515164, 18638209056768, 504541774904760, 14664951970922496, 455522635895576646, 15058911973677465600, 527896878148304296900, 19559986314930028544000, 763820398700983273655796, 31353195811771939838492672 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
R. Butler, On the Evaluation of Integral_{x=0..oo} (sin(t))^m/t^m dt by the Trapezoidal Rule, The American Mathematical Monthly, vol. 67, no. 6, 1960, pp. 566-69.
J. W. H. Swanepoel, On a generalization of a theorem by Euler, Journal of Number Theory 149 (2015) 46-56.
FORMULA
a(n) = Sum_{i=0..floor((n-1)/2)} (-1)^i*binomial(n,i)*(n-2*i)^(n-1).
a(n)/(2^n*(n-1)!) = A049330(n)/A049331(n).
a(n) = n * A099765(n). - Vladimir Reshetnikov, Sep 05 2016
MAPLE
A261398 := proc(n)
add( (-1)^i*binomial(n, i)*(n-2*i)^(n-1), i=0..floor((n-1)/2)) ;
end proc:
seq(A261398(n), n=1..25) ; # R. J. Mathar, Aug 19 2015
MATHEMATICA
Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}], {n, 1, 20}] (* Vladimir Reshetnikov, Sep 05 2016 *)
PROG
(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
CROSSREFS
Sequence in context: A357664 A321086 A111550 * A009686 A012318 A012521
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 18 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)