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A295834 Expansion of e.g.f. Product_{k>=1} (1 + x^k)^((-1)^(k+1)/k). 1

%I

%S 1,1,-1,-1,11,19,-311,-1919,20201,154169,-1363249,-14236289,140759299,

%T 1213688059,-33239720359,-257577468511,11707385639249,119005356808561,

%U -3416942071608929,-43117983466829441,893917358612502011,13133282766425234531,-411010168576899605911,-7970128344774479644991

%N Expansion of e.g.f. Product_{k>=1} (1 + x^k)^((-1)^(k+1)/k).

%e E.g.f.: Sum_{n>=0} a(n)*x^n/n! = ((1 + x)*(1 + x^3)^(1/3)*(1 + x^5)^(1/5)* ...)/((1 + x^2)^(1/2)*(1 + x^4)^(1/4)*(1 + x^6)^(1/6)* ...) = 1 + x - x^2/2! - x^3/3! + 11*x^4/4! + 19*x^5/5! - 311*x^6/6! - 1919*x^7/7! + ...

%p a:=series(mul((1+x^k)^((-1)^(k+1)/k),k=1..100),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 27 2019

%t nmax = 23; CoefficientList[Series[Product[(1 + x^k)^((-1)^(k+1)/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A028342, A168243, A206303, A284467, A294356, A295792, A295833.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Nov 28 2017

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)