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A330540
Expansion of e.g.f. Product_{k>=1} (1 + arcsinh(x^k)).
1
1, 1, 2, 11, 48, 349, 2640, 23673, 231504, 2693241, 33313680, 446104845, 6572693160, 103319528805, 1750718151000, 31865325610545, 607019625223200, 12253084499034225, 263721891513921120, 5900460781451357205, 139338570648068278200
OFFSET
0,3
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arcsinh(x^(k/d))^d / d).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcSinh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 17 2019
STATUS
approved