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A176365 Numerator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx. 2
1, 1, 11, 151, 15619, 655177, 27085381, 2330931341, 12157712239, 37307713155613, 339781108897078469, 75489558096433522049, 11482547005345338463969, 3607856726470666022715979, 18497593486903125823791655511, 520679973964725199436393399689 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The denominators are given in A176366.
Bisection of A049330. See it for further references.
LINKS
M. R. Darafsheh, Hassan Jolany, An extension of Lobachevsky formula, arXiv:1004.2653 [math.GM], 2010-2017.
FORMULA
a(n) = A049330(2*n).
EXAMPLE
a(2) = 1 because Integral_{0..infinity} (sin(x)/x)^4 dx = (1/3)*Pi.
a(3) = 11 because Integral_{0..infinity} (sin(x)/x)^6 dx = (11/40)*Pi.
a(4) = 151 because Integral_{0..infinity} (sin(x)/x)^8 dx = (151/630)*Pi.
a(5) = 15619 because Integral_{0..infinity} (sin(x)/x)^10 dx = (15619/72576)*Pi.
MAPLE
A176365 := proc(n) sin(x)^(2*n)/x^(2*n) ; int(%, x=0..infinity)/Pi ; numer(%) ; end proc: # R. J. Mathar, Apr 24 2010
MATHEMATICA
a[n_]:= (1/Pi)*Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}]//Numerator; Array[a, 16] (* Jean-François Alcover, Nov 25 2017 *)
CROSSREFS
Sequence in context: A142083 A205085 A068646 * A077577 A157186 A122769
KEYWORD
frac,nonn
AUTHOR
Jonathan Vos Post, Apr 16 2010
EXTENSIONS
5 terms added and broken URL corrected by R. J. Mathar, Apr 24 2010
Further terms from Max Alekseyev, May 07 2010
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)