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A089945
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Main diagonal of array A089944, in which the n-th row is the n-th binomial transform of the natural numbers.
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4
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1, 3, 15, 112, 1125, 14256, 218491, 3932160, 81310473, 1900000000, 49516901511, 1424099377152, 44804009850925, 1530735634132992, 56439656982421875, 2233785415175766016, 94459960699823921169, 4250383588380798812160, 202774313738037680879743
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of labeled trees on n+1 nodes with a designated node or edge. - Geoffrey Critzer, Mar 25 2017
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LINKS
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FORMULA
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a(n) = (2*n+1)*(n+1)^(n-1).
E.g.f.: (-LambertW(-x)/x)*(1-LambertW(-x))/(1+LambertW(-x)).
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MATHEMATICA
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nn = 30; T[z_] = -LambertW[-z]; Drop[Range[0, nn]! CoefficientList[Series[T[z] + T[z]^2/2, {z, 0, nn}], z], 1] (* Geoffrey Critzer, Mar 25 2017 *)
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PROG
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(PARI) a(n)=if(n<0, 0, (2*n+1)*(n+1)^(n-1))
(Magma) [(2*n+1)*(n+1)^(n-1): n in [0..50]]; // G. C. Greubel, Nov 16 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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