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A121922
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See Comments lines for definition.
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0
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-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; internal format)
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OFFSET
| 0,3
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COMMENTS
| To get this sequence evaluate the following integral for r=1,2,3,4,...:
Int(-rho*exp(-rho*s*t)*t^r*s*ln(1+t),t=0..infinity);
for rho>0 and s>0. The evaluation yields two sequences.
For, example, when r=7, the above integral is equal to:
(exp(rho*s)*( - 2520*rho^2*s^2 - 5040 + 42*rho^5*s^5 + rho^7*s^7 - 210*rho^4*s^4 + 840*rho^3*s^3 + 5040*rho*s - 7*rho^6*s^6)*Ei(1,rho*s) - 13068 + 4320*rho*s - rho^6*s^6 - 51*rho^4*s^4 + 8*rho^5*s^5 + 272*rho^3*s^3 - 1200*rho^2*s^2)/(rho^7*s^7).
The first sequence
( - 2520*rho^2*s^2 - 5040 + 42*rho^5*s^5 + rho^7*s^7 - 210*rho^4*s^4 + 840*rho^3*s^3 + 5040*rho*s - 7*rho^6*s^6)
is known (A008279 or A068424?). The second sequence produces the current entry:
( - 13068 + 4320*rho*s - rho^6*s^6 - 51*rho^4*s^4 + 8*rho^5*s^5 + 272*rho^3*s^3 - 1200*rho^2*s^2),
whose coefficients
(-1, 8, -51, 272, -1200, 4320, -13068).
give the 7th line of the triangle.
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EXAMPLE
| 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
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CROSSREFS
| The right-hand diagonal is A000254, the one before that is A001563.
Sequence in context: A178300 A081720 A137405 * A054631 A180063 A125077
Adjacent sequences: A121919 A121920 A121921 * A121923 A121924 A121925
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KEYWORD
| sign,tabl
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AUTHOR
| Arie Harel (Arie_Harel(AT)baruch.cuny.edu), Sep 09 2006
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