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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 Vincenzo Librandi, Table of n, a(n) for n = 1..200 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 Cf. A049330, A049331, A099765. Sequence in context: A357664 A321086 A111550 * A009686 A012318 A012521 Adjacent sequences: A261395 A261396 A261397 * A261399 A261400 A261401 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 18 2015 STATUS approved

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Last modified December 5 20:27 EST 2023. Contains 367594 sequences. (Running on oeis4.)