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%I #11 Dec 19 2017 18:37:58
%S 1,4,44,1912,156816,21506816,4420845376,1271132964480,487161448339712,
%T 239980527068474368,147742478026391141376,111153314734461183924224,
%U 100339775128577885016985600,107037870347952811373977239552,133204585741561810426003651444736
%N Expansion of e.g.f. arcsin(x*cosh(x)) (odd powers only).
%F a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x*cosh(x)).
%e arcsin(x*cosh(x)) = x/1! + 4*x^3/3! + 44*x^5/5! + 1912*x^7/7! + 156816*x^9/9! + ...
%t nmax = 15; Table[(CoefficientList[Series[ArcSin[x Cosh[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
%o (PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asin(x*cosh(x)))), (4^n - 1)/3) \\ _Iain Fox_, Dec 19 2017
%Y Cf. A001818, A009015, A009016, A009446, A009447, A009633, A009634, A012495, A012780, A101928, A191512, A296464, A296466, A296679, A296680, A296728, A296730, A296731, A296740.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Dec 19 2017
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