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A319174
a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k/k!)^n.
2
1, 1, 8, 90, 1448, 29750, 747462, 22182741, 759504720, 29468021238, 1277744462870, 61232148035531, 3213710056592796, 183329936018667035, 11294683874759287030, 747379761629288205795, 52864744954736491460768, 3980505280416276751035270, 317877846102688099315299678
OFFSET
0,3
FORMULA
a(n) = n! * [x^n] exp(n*Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(j!)^k)).
MATHEMATICA
Table[n! SeriesCoefficient[Product[1/(1 - x^k/k!)^n, {k, 1, n}], {x, 0, n}], {n, 0, 18}]
Table[n! SeriesCoefficient[Exp[n Sum[Sum[x^(j k)/(k (j!)^k), {j, 1, n}], {k, 1, n}]], {x, 0, n}], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 12 2018
STATUS
approved