A295833 Expansion of e.g.f. Product_{k>=1} (1 + x^k)^((-1)^k/k).

1, -1, 3, -11, 47, -279, 2089, -16057, 137409, -1417553, 15656651, -187422531, 2501688463, -34832785831, 529520417217, -8723102543009, 146573712239489, -2670058109819937, 52017332039568019, -1041334898093864443, 22335551258991482991, -502509800119879530551, 11641825391540821682393

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Example

E.g.f.: Sum_{n>=0} a(n)*x^n/n! = ((1 + x^2)^(1/2)*(1 + x^4)^(1/4)*(1 + x^6)^(1/6)* ...)/((1 + x)*(1 + x^3)^(1/3)*(1 + x^5)^(1/5)* ...) = 1 - x + 3*x^2/2! - 11*x^3/3! + 47*x^4/4! - 279*x^5/5! + 2089*x^6/6! - 16057*x^7/7! + ...

Maple

a:=series(mul((1+x^k)^((-1)^k/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[(1 + x^k)^((-1)^k/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A028342, A168243, A206303, A284474, A294356, A295792, A295834.

Sequence in context: A020543 A111139 A167564 * A191344 A374983 A308538

Adjacent sequences: A295830 A295831 A295832 * A295834 A295835 A295836

Keyword

sign

Author

Ilya Gutkovskiy, Nov 28 2017

Status

approved