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A321265
a(n) = [x^n] Product_{k>=1} (1 + x^k)^J_n(k), where J_() is the Jordan function.
1
1, 1, 3, 33, 425, 12083, 665707, 68834806, 13654633905, 5535319947544, 4371956013518511, 6700051541666225780, 21029477920140943174285, 131152064162504305814647983, 1603485136950993248524876767297, 40291404321882574322412345562762188, 2031269423141309839019651314585293713041
OFFSET
0,3
FORMULA
a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} Sum_{j|d} (-1)^(k/d+1)*d*j^n*mu(d/j) ) * x^k/k).
MATHEMATICA
Table[SeriesCoefficient[Product[(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[(-1)^(k/d + 1) 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