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%I #12 Aug 05 2023 04:36:21
%S 105,13440,229635,1720320,8203125,29393280,86472015,220200960,
%T 502211745,1050000000,2046152955,3762339840,6588594285,11068417920,
%U 17940234375,28185722880,43085560665,64283103360,93856532595,134400000000
%N Denominator of I(n)=integral_{x=0 to 1/n}(x^2-1)^3 dx.
%C The numerator is b(n) = -105*n^6+105*n4-63*n^2+15. E.g., b(3) = -68392.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F a(n) = 105*n^7 = 105*A001015(n).
%F G.f.: 105*x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^8. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%e I(3) = -68592/229635.
%t f[n_] := Integrate[(x^2 - 1)^3, {x, 0, 1/n}]; Table[(-105n^6 + 105n^4 - 63n^2 + 15)/f[n], {n, 20}] (* _Robert G. Wilson v_, May 03 2004 *)
%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{105,13440,229635,1720320,8203125,29393280,86472015,220200960},20] (* _Harvey P. Dale_, Aug 04 2023 *)
%K nonn,easy
%O 1,1
%A Al Hakanson (hawkuu(AT)excite.com), Apr 29 2004
%E More terms from _Robert G. Wilson v_, May 03 2004
%E G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009
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