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%I #21 Mar 26 2022 13:41:01
%S 1,3,18,165,2016,30783,564048,12057825,294587136,8096756763,
%T 247266851328,8306410495485,304403359942656,12085026305182743,
%U 516690458532292608,23668814542820609145,1156515067746149400576,60041982382475841900723,3300519734382436473765888
%N Expansion of e.g.f. 1/(1-3*sinh(x)).
%H Seiichi Manyama, <a href="/A107403/b107403.txt">Table of n, a(n) for n = 0..379</a>
%F a(n) ~ n!/(sqrt(10)*(log(1/3+sqrt(10)/3))^(n+1)). - _Vaclav Kotesovec_, Jun 26 2013
%F a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * a(n-2*k-1). - _Ilya Gutkovskiy_, Mar 10 2022
%p E(x):=1/(1-3*sinh(x)): f[0]:=E(x): for n from 1 to 30 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..30);
%t CoefficientList[Series[1/(1-3*Sinh[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*sinh(x)))) \\ _Seiichi Manyama_, Mar 26 2022
%Y Cf. A000557, A006154.
%K nonn
%O 0,2
%A _Miklos Kristof_, Jun 09 2005
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