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A308023 G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 - x)) * (A(x/(1 - x)) + A(x^2/(1 - x)^2) + A(x^3/(1 - x)^3) + ...)). 1

%I

%S 1,1,4,14,52,208,908,4304,22016,120796,706896,4389752,28800668,

%T 198884648,1440809932,10918549748,86331306980,710609746752,

%U 6076740094448,53887906573064,494734785732236,4695242718593096,45998992617959932,464614423225361404,4832633949407618644

%N G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 - x)) * (A(x/(1 - x)) + A(x^2/(1 - x)^2) + A(x^3/(1 - x)^3) + ...)).

%F a(1) = 1; a(n+1) = Sum_{k=1..n} binomial(n,k) * Sum_{d|k} a(d).

%t terms = 25; A[_] = 0; Do[A[x_] = x (1 + 1/(1 - x) Sum[A[x^k/(1 - x)^k], {k, 1, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]

%t a[n_] := a[n] = Sum[Binomial[n - 1, k] Sum[a[d], {d, Divisors[k]}], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 25}]

%Y Cf. A003238, A040027, A308024.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 09 2019

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Last modified May 21 03:10 EDT 2022. Contains 353886 sequences. (Running on oeis4.)