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A059606
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Expansion of (1/2)*(exp(2*x)-1)*exp(exp(x)-1).
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8
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0, 1, 4, 16, 68, 311, 1530, 8065, 45344, 270724, 1709526, 11376135, 79520644, 582207393, 4453142140, 35500884556, 294365897104, 2533900264547, 22604669612078, 208656457858161, 1990060882027600
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OFFSET
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0,3
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COMMENTS
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Starting (1, 4, 16, 68, 311, ...), = A008277 * A000217, i.e., the product of the Stirling2 triangle and triangular series. - Gary W. Adamson, Jan 31 2008
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n} Stirling2(n, i)*binomial(i+1, 2).
G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/Product_{j=1..k} (1 - j*x). - Ilya Gutkovskiy, Jun 19 2018
a(n) ~ n^2 * Bell(n) / (2*LambertW(n)^2) * (1 - LambertW(n)/n). - Vaclav Kotesovec, Jul 28 2021
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MAPLE
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s := series(1/2*(exp(2*x)-1)*exp(exp(x)-1), x, 21): for i from 0 to 20 do printf(`%d, `, i!*coeff(s, x, i)) od:
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[((Exp[2x]-1)Exp[Exp[x]-1])/2, {x, 0, nn}] , x] Range[0, nn]!] (* Harvey P. Dale, Nov 10 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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