OFFSET
0,9
LINKS
D. J. Broadhurst, Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, sequence gamma_{3,j}^(A).
FORMULA
Product_n (1-x^n)^{a(n)} = 1-x-x^4; equivalently, a(n) = (1/n) sum_{ d divides n } mu(n/d) A014097(d).
MATHEMATICA
max = 50; ClearAll[a]; coes = CoefficientList[ Series[ Product[ (1-x^n)^a[n-1], {n, 0, max}] - (1-x-x^4), {x, 0, max}] /. 0^_ -> 1, x]; eq = Rest[ Thread[ coes == 0]]; s[1] = Solve[ eq[[1]], a[0]][[1]]; a[0] = a[0] /. s[1][[1]]; Print[a[0]]; Do[ eq = Rest[eq] /. s[n]; s[n+1] = Solve[ eq[[1]], a[n]][[1]]; a[n] = a[n] /. s[n+1][[1]]; Print[a[n]], {n, 1, max-1}]; A020999 = Table[ a[n], {n, 0, max-1}](* From Jean-François Alcover, Jan 31 2012, after formula *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved