# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a176365 Showing 1-1 of 1 %I A176365 #20 Dec 13 2019 05:54:43 %S A176365 1,1,11,151,15619,655177,27085381,2330931341,12157712239, %T A176365 37307713155613,339781108897078469,75489558096433522049, %U A176365 11482547005345338463969,3607856726470666022715979,18497593486903125823791655511,520679973964725199436393399689 %N A176365 Numerator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx. %C A176365 The denominators are given in A176366. %C A176365 Bisection of A049330. See it for further references. %H A176365 G. C. Greubel, Table of n, a(n) for n = 1..75 %H A176365 M. R. Darafsheh, Hassan Jolany, An extension of Lobachevsky formula, arXiv:1004.2653 [math.GM], 2010-2017. %F A176365 a(n) = A049330(2*n). %e A176365 a(2) = 1 because Integral_{0..infinity} (sin(x)/x)^4 dx = (1/3)*Pi. %e A176365 a(3) = 11 because Integral_{0..infinity} (sin(x)/x)^6 dx = (11/40)*Pi. %e A176365 a(4) = 151 because Integral_{0..infinity} (sin(x)/x)^8 dx = (151/630)*Pi. %e A176365 a(5) = 15619 because Integral_{0..infinity} (sin(x)/x)^10 dx = (15619/72576)*Pi. %p A176365 A176365 := proc(n) sin(x)^(2*n)/x^(2*n) ; int(%,x=0..infinity)/Pi ; numer(%) ; end proc: # _R. J. Mathar_, Apr 24 2010 %t A176365 a[n_]:= (1/Pi)*Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}]//Numerator; Array[a, 16] (* _Jean-François Alcover_, Nov 25 2017 *) %Y A176365 Cf. A049330, A176366. %K A176365 frac,nonn %O A176365 1,3 %A A176365 _Jonathan Vos Post_, Apr 16 2010 %E A176365 5 terms added and broken URL corrected by _R. J. Mathar_, Apr 24 2010 %E A176365 Further terms from _Max Alekseyev_, May 07 2010 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE