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Search: id:A042977
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| A042977 |
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Triangle of coefficients of n-th derivative of Lambert function W (Mathematica's ProductLog). |
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8
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| 1, -2, -1, 9, 8, 2, -64, -79, -36, -6, 625, 974, 622, 192, 24, -7776, -14543, -11758, -5126, -1200, -120, 117649, 255828, 248250, 137512, 45756, 8640, 720, -2097152, -5187775, -5846760, -3892430, -1651480, -445572, -70560, -5040
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Eric Weisstein's World of Mathematics, Lambert W-Function
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FORMULA
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E.g.f.: (LambertW(exp(x)*(x+y*(1+x)^2))-x)/(1+x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 19 2003
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EXAMPLE
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1; -2 - W; 9 + 8 W + 2 W^2; -64 - 79 W - 36 W^2 - 6 W^3; 625 + 974 W + 622 W^2 + 192 W^3 + 24 W^4; ...
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MATHEMATICA
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Table[ Simplify[ (Evaluate[ D[ ProductLog[ z ], {z, n} ] ]/ .ProductLog[ z ]->W)*z^n/W^n (1+W)^(2n-1) ], {n, 12} ];
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CROSSREFS
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Cf. A013703 (twice row sums), A000444, A000525, A064781, A064785, A064782.
First column A000169, main diagonal A000142, first subdiagonal A052582.
Sequence in context: A021459 A133169 A133175 this_sequence A108290 A108291 A019615
Adjacent sequences: A042974 A042975 A042976 this_sequence A042978 A042979 A042980
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KEYWORD
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sign
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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