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

1,1

Comments

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

Links

Table of n, a(n) for n=1..20.

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

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

Example

I(3) = -68592/229635.

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 *)

Crossrefs

Sequence in context: A263888 A269474 A255497 * A199519 A082368 A001546

Adjacent sequences: A094072 A094073 A094074 * A094076 A094077 A094078

Keyword

nonn,easy

Author

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

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

Status

approved