A303004 Expansion of e.g.f. exp(Sum_{k>=1} M(k)*x^k/k!), where M() is the exponential of Mangoldt function (A014963).

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

Author

Ilya Gutkovskiy, Apr 17 2018

Keywords

• nonn

Comments

Exponential transform of A014963.

Examples

			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! + ...
		

Links

• Eric Weisstein's World of Mathematics, Mangoldt Function
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A014963, A140254, A140255.

Programs

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}]

Formula

E.g.f.: exp(Sum_{k>=1} A014963(k)*x^k/k!).