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 A168243 Expansion of e.g.f. Product_{i>=1} (1 + x^i)^(1/i). 18
 1, 1, 1, 5, 11, 59, 439, 2659, 13705, 160649, 2009681, 16966421, 183312931, 2078169235, 34203787591, 657685416179, 8054585463569, 104530824746129, 2595754682459425, 39767021562661669, 758079429084897211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..446 Vaclav Kotesovec, Graph: (a(n)/n!) / (n^(log(2) - 1)), 250000 terms FORMULA E.g.f.: exp(Sum_{n>=1} A048272(n)*x^n/n). Conjecture: log(a(n)/n!) ~ (log(2) - 1) * log(n). - Vaclav Kotesovec, Sep 10 2018 MAPLE a:=series(mul((1+x^i)^(1/i), i=1..100), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 28 2019 MATHEMATICA nmax=20; CoefficientList[Series[Product[(1+x^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 28 2015 *) a[n_] := a[n] = If[n == 0, 1, Sum[Sum[-(-1)^d, {d, Divisors[k]}]*a[n-k], {k, 1, n}]/n]; Table[n!*a[n], {n, 0, 20}] (* Vaclav Kotesovec, Sep 07 2018 *) CROSSREFS Cf. A028342. Sequence in context: A208768 A057824 A057822 * A173875 A095150 A215759 Adjacent sequences:  A168240 A168241 A168242 * A168244 A168245 A168246 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Nov 21 2009 STATUS approved

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)