A094075 Denominator of I(n)=integral_{x=0 to 1/n}(x^2-1)^3 dx.

105, 13440, 229635, 1720320, 8203125, 29393280, 86472015, 220200960, 502211745, 1050000000, 2046152955, 3762339840, 6588594285, 11068417920, 17940234375, 28185722880, 43085560665, 64283103360, 93856532595, 134400000000

Offset: 1

Author

Al Hakanson (hawkuu(AT)excite.com), Apr 29 2004

Keywords

• nonn
• easy

Comments

The numerator is b(n) = -105*n^6+105*n4-63*n^2+15. E.g., b(3) = -68392.

Examples

			I(3) = -68592/229635.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Programs

Mathematica

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 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{105,13440,229635,1720320,8203125,29393280,86472015,220200960},20] (* Harvey P. Dale, Aug 04 2023 *)

Formula

a(n) = 105*n^7 = 105*A001015(n).

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

Extensions

More terms from Robert G. Wilson v, May 03 2004

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009