OFFSET
0,3
EXAMPLE
At j=7, the result of the integration Integral_{t=0..oo} -rho*exp(-rho*s*t)*t^j*s*log(1+t) dt
can be written as (F(u,7)*exp(u)*Ei(1,u) + G(u,7))/u^7, where
F(u,7) = u^7 - 7*u^6 + 42*u^5 - 210*u^4 + 840*u^3 -2520*u^2 + 5040*u - 5040,
G(u,7) = - u^6 + 8*u^5 - 51*u^4 + 272*u^3 - 1200*u^2 + 4320*u - 13068,
and u=rho*s.
The coefficients of F(u,7), i.e., (1, -7, 42, -210, 840, 2520, 5040, -5040), comprise the 7th row of A008279 (see also A068424). The coefficients of G(u,7), i.e., (-1, 8, -51, 272, -1200, 4320, -13068) give the 7th row of the triangle below.
Triangle begins:
-1
1, -3
-1, 4, -11
1, -5, 18, -50
-1, 6, -27, 96, -274
1, -7, 38, -168, 600, -1764
-1, 8, -51, 272, -1200, 4320, -13068
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Arie Harel, Sep 09 2006
EXTENSIONS
Edited by Jon E. Schoenfield, Oct 20 2013
STATUS
approved