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

0,3

Comments

Exponential transform of A014963.

Links

Table of n, a(n) for n=0..23.

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

Cf. A014963, A140254, A140255.

Sequence in context: A307593 A351144 A221973 * A054912 A093463 A302989

Adjacent sequences: A303001 A303002 A303003 * A303005 A303006 A303007

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 17 2018

Status

approved