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A321263
a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^(2*k)/(1 - x^k)).
1
1, 0, 1, 1, 18, 3, 926, 264, 146255, 64190, 138356840, 22816773, 509079790798, 108923489863, 6757117812676818, 1403337110700033, 474610323092906351464, 52144014892723916074, 130074987349483695192896881, 14487112805054799566652854, 132992779975091800967037313578152
OFFSET
0,5
FORMULA
a(n) = [x^n] 1/(1 - Sum_{k>=1} (sigma_n(k) - k^n)*x^k).
a(n) = [x^n] 1/(1 - Sum_{k>=1} (k^n - J_n(k))*x^k/(1 - x^k)), where J_() is the Jordan function.
MATHEMATICA
Table[SeriesCoefficient[1/(1 - Sum[k^n x^(2 k)/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - Sum[(DivisorSigma[n, k] - k^n) x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - Sum[(k^n - Sum[d^n MoebiusMu[k/d], {d, Divisors[k]}]) x^k/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 01 2018
STATUS
approved