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a(n) = n! * [x^n] exp(n*sinh(x)).
3

%I #8 Sep 29 2017 20:35:56

%S 1,1,4,30,320,4380,73152,1443008,32837632,846829008,24406425600,

%T 777438110240,27122380259328,1028481186011968,42119646804852736,

%U 1852697321086064640,87113569172046479360,4360314205952755126528,231474221309788621111296,12990330117363343153415680

%N a(n) = n! * [x^n] exp(n*sinh(x)).

%H Robert Israel, <a href="/A293022/b293022.txt">Table of n, a(n) for n = 0..380</a>

%p N:= 30: # to get a(0)..a(N)

%p S:= series(exp(n*sinh(x)),x,N+1):

%p seq(n!*coeff(S,x,n),n=0..N); # _Robert Israel_, Sep 29 2017

%t Table[n! SeriesCoefficient[Exp[n Sinh[x]], {x, 0, n}], {n, 0, 19}]

%Y Cf. A003724, A134200.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 28 2017