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

1, 1, -1, -1, 11, 19, -311, -1919, 20201, 154169, -1363249, -14236289, 140759299, 1213688059, -33239720359, -257577468511, 11707385639249, 119005356808561, -3416942071608929, -43117983466829441, 893917358612502011, 13133282766425234531, -411010168576899605911, -7970128344774479644991

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Example

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! + ...

Maple

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

Mathematica

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

Crossrefs

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

Sequence in context: A163151 A020457 A032370 * A129908 A344431 A129909

Adjacent sequences: A295831 A295832 A295833 * A295835 A295836 A295837

Keyword

sign

Author

Ilya Gutkovskiy, Nov 28 2017

Status

approved