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A352327 Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).

%I A352327 #19 Mar 25 2022 10:18:21
%S A352327 1,1,4,19,130,1081,10894,127639,1711210,25798141,432212134,7964801659,
%T A352327 160121522290,3487254825601,81790592435374,2055350489070079,
%U A352327 55093108433421370,1569052795651631461,47315282424232826614,1506074331671551028899
%N A352327 Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).
%H A352327 Seiichi Manyama, <a href="/A352327/b352327.txt">Table of n, a(n) for n = 0..414</a>
%F A352327 a(0) = 1; a(n) = Sum_{k=1..n} (3+(-1)^k)/2 * binomial(n,k) * a(n-k).
%F A352327 a(n) ~ n! / (sqrt(6) * log(1 + sqrt(2/3))^(n+1)). - _Vaclav Kotesovec_, Mar 12 2022
%p A352327 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A352327       a(n-k)*binomial(n, k)*(2-(k mod 2)), k=1..n))
%p A352327     end:
%p A352327 seq(a(n), n=0..19); # _Alois P. Heinz_, Mar 25 2022
%t A352327 m = 19; Range[0, m]! * CoefficientList[Series[1/(3 - Exp[x] - Cosh[x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352327 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(x)-cosh(x))))
%o A352327 (PARI) a(n) = if(n==0, 1, sum(k=1, n, (3+(-1)^k)/2*binomial(n, k)*a(n-k)));
%Y A352327 Cf. A000670, A006154, A094088, A352326, A352624.
%K A352327 nonn
%O A352327 0,3
%A A352327 _Seiichi Manyama_, Mar 12 2022