OFFSET
1,1
COMMENTS
The numerator is b(n) = -105*n^6+105*n4-63*n^2+15. E.g., b(3) = -68392.
LINKS
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
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