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A295794 Expansion of e.g.f. Product_{k>=1} exp(x^k/(1 + x^k)). 3
1, 1, 1, 13, 25, 241, 2761, 14701, 153553, 1903105, 27877681, 263555821, 4788201001, 65083782193, 1040877257785, 24098794612621, 373918687272481, 7393663746307201, 164894196647876833, 3504497611085823565, 81863829346282866361, 2257321249626793901041, 49755091945025205954601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

FORMULA

E.g.f.: exp(Sum_{k>=1} A048272(k)*x^k).

E.g.f.: exp(x*f'(x)), where f(x) = log(Product_{k>=1} (1 + x^k)^(1/k)).

a(n) ~ exp(2*sqrt(n*log(2)) - 1/4 - n) * n^(n - 1/4) * log(2)^(1/4) / sqrt(2). - Vaclav Kotesovec, Sep 07 2018

MAPLE

a:=series(mul(exp(x^k/(1+x^k)), k=1..100), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 27 2019

MATHEMATICA

nmax = 22; CoefficientList[Series[Product[Exp[x^k/(1 + x^k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 22; CoefficientList[Series[Exp[x D[Log[Product[(1 + x^k)^(1/k), {k, 1, nmax}]], x]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[-k Sum[(-1)^d, {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 22}]

CROSSREFS

Cf. A028342, A048272, A168243, A206303, A294363, A294392, A295739.

Sequence in context: A301327 A116524 A053404 * A122003 A123827 A105796

Adjacent sequences:  A295791 A295792 A295793 * A295795 A295796 A295797

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 27 2017

STATUS

approved

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Last modified August 10 04:27 EDT 2022. Contains 356029 sequences. (Running on oeis4.)