A330534 Expansion of e.g.f. Product_{k>=1} 1 / (1 - arcsin(x^k)).
1, 1, 4, 19, 128, 929, 9008, 88677, 1068496, 13585713, 195465552, 2962147101, 50411419368, 887757722409, 17125724016984, 346462040798229, 7503508038803616, 169554609033560673, 4085808543521351136, 102156453049201047981
Offset: 0
Keywords
Programs
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Mathematica
nmax = 19; CoefficientList[Series[Product[1/(1 - ArcSin[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! nmax = 19; CoefficientList[Series[Exp[Sum[Sum[ArcSin[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
Formula
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arcsin(x^(k/d))^d / d).