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A308564
Expansion of e.g.f. Sum_{k>=1} phi(k)*(exp(x) - 1)^k/k!, where phi = Euler totient function (A000010).
1
1, 2, 6, 22, 90, 404, 1974, 10366, 57864, 341690, 2134022, 14104624, 98498972, 723664482, 5561589508, 44473028634, 368602225688, 3159852790392, 27997141025686, 256410638073082, 2428063270357748, 23774001479212114, 240580239864321604, 2513553050765310236
OFFSET
1,2
COMMENTS
Stirling transform of A000010.
LINKS
FORMULA
G.f.: Sum_{k>=1} phi(k)*x^k / Product_{j=1..k} (1 - j*x).
a(n) = Sum_{k=1..n} Stirling2(n,k)*phi(k).
MAPLE
b:= proc(n, m) option remember; uses numtheory;
`if`(n=0, phi(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=1..24); # Alois P. Heinz, Aug 04 2021
MATHEMATICA
nmax = 24; Rest[CoefficientList[Series[Sum[EulerPhi[k] (Exp[x] - 1)^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
nmax = 24; Rest[CoefficientList[Series[Sum[EulerPhi[k] x^k/Product[(1 - j x), {j, 1, k}], {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Sum[StirlingS2[n, k] EulerPhi[k], {k, 1, n}], {n, 1, 24}]
CROSSREFS
Sequence in context: A089449 A264601 A374551 * A226435 A292318 A150271
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 07 2019
STATUS
approved