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A094075 Denominator of I(n)=integral_{x=0 to 1/n}(x^2-1)^3 dx. 0
105, 13440, 229635, 1720320, 8203125, 29393280, 86472015, 220200960, 502211745, 1050000000, 2046152955, 3762339840, 6588594285, 11068417920, 17940234375, 28185722880, 43085560665, 64283103360, 93856532595, 134400000000 (list; graph; refs; listen; history; text; internal format)
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.

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 *)

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

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

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

STATUS

approved

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Last modified May 21 17:51 EDT 2022. Contains 353921 sequences. (Running on oeis4.)