Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Mar 22 2018 17:58:04
%S 1,1,4,14,68,362,2224,14940,110348,878600,7518002,68529122,662709832,
%T 6764329158,72622813172,817239648500,9612724174088,117878757097178,
%U 1503660164683864,19911519090176808,273221610513382028,3878513600608651636,56873187579428449852,860296560100458300892
%N Expansion of e.g.f. exp(Sum_{k>=1} psi(k)*x^k/k!), where psi() is the Dedekind psi function (A001615).
%C Exponential transform of A001615.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F E.g.f.: exp(Sum_{k>=1} A001615(k)*x^k/k!).
%e E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 14*x^3/3! + 68*x^4/4! + 362*x^5/5! + 2224*x^6/6! + 14940*x^7/7! + ...
%t psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]; a[n_] := a[n] = SeriesCoefficient[Exp[Sum[psi[k] x^k/k!, {k, 1, n}]], {x, 0, n}]; Table[a[n] n!, {n, 0, 23}]
%t psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]; a[n_] := a[n] = Sum[psi[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
%Y Cf. A001615, A063659, A156303, A300011.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 22 2018