A296048 Expansion of e.g.f. Product_{k>=1} ((1 - x^k)/(1 + x^k))^(1/k).

1, -2, 2, -4, 32, -128, 496, -2336, 29312, -395776, 3194624, -21951488, 277270528, -4027191296, 38850203648, -739834458112, 19460560584704, -299971773661184, 3169121209090048, -51853341314514944, 1234704403684130816, -30653318499154788352, 658369600764729884672, -10809496145754051313664

Offset: 0

Author

Ilya Gutkovskiy, Dec 03 2017

Keywords

• sign

Crossrefs

Cf. A001227, A028342, A028343, A054844, A156616, A168243, A285675, A294356, A295792.

Programs

Maple

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

Mathematica

nmax = 23; CoefficientList[Series[Product[((1 - x^k)/(1 + x^k))^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Exp[-2 Sum[Total[Mod[Divisors[k], 2] x^k]/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: exp(-2*Sum_{k>=1} A001227(k)*x^k/k).

E.g.f.: exp(-Sum_{k>=1} A054844(k)*x^k/k).