The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #5 Dec 17 2019 19:14:19
%S 1,1,2,11,48,349,2640,23673,231504,2693241,33313680,446104845,
%T 6572693160,103319528805,1750718151000,31865325610545,607019625223200,
%U 12253084499034225,263721891513921120,5900460781451357205,139338570648068278200
%N Expansion of e.g.f. Product_{k>=1} (1 + arcsinh(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arcsinh(x^(k/d))^d / d).
%t nmax = 20; CoefficientList[Series[Product[(1 + ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t 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]!
%Y Cf. A001818, A270294, A330539.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019