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A352326 Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).

%I A352326 #21 Mar 25 2022 10:16:36
%S A352326 1,2,9,62,567,6482,88929,1423382,26037027,535813802,12251630349,
%T A352326 308153112302,8455276083087,251333936555522,8045613346221369,
%U A352326 275950004166050822,10095559110771678747,392427366313299119642,16151459739717643489989
%N A352326 Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).
%H A352326 Seiichi Manyama, <a href="/A352326/b352326.txt">Table of n, a(n) for n = 0..395</a>
%F A352326 a(0) = 1; a(n) = Sum_{k=1..n} (3-(-1)^k)/2 * binomial(n,k) * a(n-k).
%F A352326 a(n) ~ n! / (sqrt(7) * log((2 + sqrt(7))/3)^(n+1)). - _Vaclav Kotesovec_, Mar 12 2022
%p A352326 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A352326       a(n-k)*binomial(n, k)*(1+(k mod 2)), k=1..n))
%p A352326     end:
%p A352326 seq(a(n), n=0..18); # _Alois P. Heinz_, Mar 25 2022
%t A352326 m = 18; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - Sinh[x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352326 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-sinh(x))))
%o A352326 (PARI) a(n) = if(n==0, 1, sum(k=1, n, (3-(-1)^k)/2*binomial(n, k)*a(n-k)));
%Y A352326 Cf. A000670, A006154, A028296, A094088, A352327, A352617.
%K A352326 nonn
%O A352326 0,2
%A A352326 _Seiichi Manyama_, Mar 12 2022