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%I #13 Mar 24 2023 10:29:12
%S 1,3,9,36,189,1068,6669,47568,363897,2976048,26422929,248498880,
%T 2464625205,25922981568,285884886933,3296418423552,39795656126193,
%U 499998631895808,6526830528863001,88493793850020864,1241919513823360941,18020032474632956928
%N Expansion of e.g.f. exp(3 * x * cosh(x)).
%F E.g.f.: exp(3 * x * cosh(x)).
%F a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%t With[{m = 21}, Range[0, m]! * CoefficientList[Series[Exp[3*x*Cosh[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*x*cosh(x))))
%o (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y Cf. A003727, A352644.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 25 2022
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