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A300011 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)*x^k/k!), where phi() is the Euler totient function (A000010). 3
1, 1, 2, 6, 20, 80, 362, 1820, 10084, 60522, 391864, 2714514, 20001700, 156107224, 1284705246, 11112088358, 100698613720, 953478331288, 9410963022318, 96614921664444, 1029705968813656, 11373102766644372, 129972789566984682, 1534638410054873892, 18696544357738885720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Exponential transform of A000010.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..552

N. J. A. Sloane, Transforms

FORMULA

E.g.f.: exp(Sum_{k>=1} A000010(k)*x^k/k!).

EXAMPLE

E.g.f.: A(x) = 1 + x/1! + 2*x^2/2! + 6*x^3/3! + 20*x^4/4! + 80*x^5/5! + 362*x^6/6! + 1820*x^7/7! + ...

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*

      binomial(n-1, j-1)*numtheory[phi](j), j=1..n))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Mar 09 2018

MATHEMATICA

nmax = 24; CoefficientList[Series[Exp[Sum[EulerPhi[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Sum[EulerPhi[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]

CROSSREFS

Cf. A000010, A050392, A159929, A274804, A295739.

Sequence in context: A187009 A144168 A177482 * A242154 A108124 A186365

Adjacent sequences:  A300008 A300009 A300010 * A300012 A300013 A300014

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 09 2018

STATUS

approved

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Last modified October 27 11:51 EDT 2021. Contains 348276 sequences. (Running on oeis4.)