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 A078751 Triangle read by rows: ss(m,k) = normalized partial derivative of (t,z)->exp(t g(z)) at (0,0), where 2 g(z)=1+exp(-2 z g(z)). 0
 2, 4, 8, 24, 48, 48, 224, 480, 576, 384, 2880, 6400, 8640, 7680, 3840, 47232, 107520, 155520, 161280, 115200, 46080, 942592, 2182656, 3306240, 3763200, 3225600, 1935360, 645120, 22171648, 51996672, 81414144, 98703360, 94617600, 69672960 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let g(z) = 1/2 + W(z/e^z)/(2 z), where W is Lambert's W-function; g satisfies 2 g(z)=1+exp(-2 z g(z)). Let c(m,n) be the coefficient of z^m in the Maclaurin series for g(z)^n; equivalently c(m,n) is 1/m! times the mixed partial derivative (d^(m+n) f(t,z))/(dz^m dt^n), where f(t,z) = exp(t g(z)). For 0=1) is A038049. Sequence in context: A226659 A009327 A027168 * A290859 A290659 A286866 Adjacent sequences: A078748 A078749 A078750 * A078752 A078753 A078754 KEYWORD nonn,tabl,easy AUTHOR Carmen Chicone (carmen(AT)chicone.math.missouri.edu), Dec 22 2002 EXTENSIONS Edited by Dean Hickerson, Dec 30 2002 STATUS approved

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Last modified March 28 06:07 EDT 2023. Contains 361577 sequences. (Running on oeis4.)