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A303004
Expansion of e.g.f. exp(Sum_{k>=1} M(k)*x^k/k!), where M() is the exponential of Mangoldt function (A014963).
0
1, 1, 3, 10, 39, 186, 962, 5587, 35367, 241216, 1771052, 13827925, 114558314, 1001769237, 9208116647, 88737108635, 893505145271, 9379190223746, 102402586369892, 1160487000658679, 13627075242031720, 165524499516422471, 2076762033563394443, 26877177548737581587
OFFSET
0,3
COMMENTS
Exponential transform of A014963.
LINKS
Eric Weisstein's World of Mathematics, Mangoldt Function
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: exp(Sum_{k>=1} A014963(k)*x^k/k!).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 3*x^2/2! + 10*x^3/3! + 39*x^4/4! + 186*x^5/5! + 962*x^6/6! + 5587*x^7/7! + ...
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[Sum[Exp[MangoldtLambda[k]] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Exp[MangoldtLambda[k]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 17 2018
STATUS
approved