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A121922 The result of the integration of (-rho*exp(-rho*s*t)*t^j*s*log(1+t),t=0..infinity) can be written as (F(u,j)*exp(u)*Ei(1,u) + G(u,j))/u^j, where rho>0, s>0, and u=rho*s. Sequence is the regular triangle corresponding to G(u,j). 0
-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, 1, -9, 66, -414, 2200, -9720, 35280, -109584, -1, 10, -83, 600, -3750, 19920, -88200, 322560, -1026576, 1, -11, 102, -836, 6024, -37620, 199920, -887040, 3265920, -10628640 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

At j=7, the result of the integration

Integral(-rho*exp(-rho*s*t)*t^j*s*log(1+t),t=0..infinity

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

The right-hand diagonal is A000254, the one before that is A001563.

Sequence in context: A322456 A301701 A262078 * A054631 A180063 A125077

Adjacent sequences:  A121919 A121920 A121921 * A121923 A121924 A121925

KEYWORD

sign,tabl

AUTHOR

Arie Harel, Sep 09 2006

EXTENSIONS

Edited by Jon E. Schoenfield, Oct 20 2013

STATUS

approved

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Last modified April 24 22:03 EDT 2019. Contains 322446 sequences. (Running on oeis4.)