A346545 - OEIS

%I #8 Sep 16 2021 23:52:43

%S 1,1,5,26,175,1384,12933,135050,1582901,20380208,286577757,4352682256,

%T 71247772121,1244923243966,23166410620637,456940648889070,

%U 9521696033968393,208851154175983608,4812156417656806393,116112764199821653284,2928658457243240595901,77042063713731887400418

%N E.g.f.: Product_{k>=1} 1 / (1 - x^k)^(exp(x)/k).

%C Exponential transform of A002746.

%F E.g.f.: exp( exp(x) * Sum_{k>=1} d(k) * x^k / k ).

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002746(k) * a(n-k).

%t nmax = 21; CoefficientList[Series[Product[1/(1 - x^k)^(Exp[x]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%t nmax = 21; CoefficientList[Series[Exp[Exp[x] Sum[DivisorSigma[0, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

%t A002746[n_] := Sum[Binomial[n, k] DivisorSigma[0, k] (k - 1)!, {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A002746[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

%Y Cf. A000005, A002746, A028342, A346546, A346547, A346548.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 16 2021