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A321264
a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^J_n(k), where J_() is the Jordan function.
1
1, 1, 4, 34, 456, 12388, 677244, 69513187, 13727785600, 5551190294478, 4378921597198116, 6705804947252051188, 21038823519531799964724, 131183284379709847290156854, 1603688086811508900855649976528, 40293997364837932973226463649637881, 2031337795407293560044987268598542021504
OFFSET
0,3
FORMULA
a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} Sum_{j|d} d*j^n*mu(d/j) ) * x^k/k).
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - x^k)^Sum[d^n MoebiusMu[k/d], {d, Divisors[k]}], {k, 1, n}], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[Exp[Sum[Sum[Sum[d j^n MoebiusMu[d/j], {j, Divisors[d]}], {d, Divisors[k]}] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 01 2018
STATUS
approved