A300011 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)*x^k/k!), where phi() is the Euler totient function (A000010).
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
Offset: 0
Keywords
Examples
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! + ...
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..552
- N. J. A. Sloane, Transforms
Programs
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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}] -
PARI
a(n) = if(n==0, 1, sum(k=1, n, eulerphi(k)*binomial(n-1, k-1)*a(n-k))); \\ Seiichi Manyama, Feb 27 2022
Formula
E.g.f.: exp(Sum_{k>=1} A000010(k)*x^k/k!).
a(0) = 1; a(n) = Sum_{k=1..n} phi(k) * binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, Feb 27 2022
Comments