A349105 - OEIS

%I #22 Mar 28 2022 07:42:48

%S 1,1,2,8,40,243,1796,15502,152608,1690613,20814208,281859540,

%T 4163795648,66636761575,1148477490304,21207704998010,417728195909632,

%U 8742243282090153,193720478508563456,4531158728871170080,111562803180301643776,2884156736234559267611

%N Expansion of e.g.f. 1/(1 - (sinh(x) + x*cosh(x))/2 ).

%H Seiichi Manyama, <a href="/A349105/b349105.txt">Table of n, a(n) for n = 0..435</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (k+1) * binomial(n,2*k+1) * a(n-2*k-1).

%t With[{m = 21}, Range[0, m]! * CoefficientList[Series[1/(1 - (Sinh[x] + x*Cosh[x])/2), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-(sinh(x)+x*cosh(x))/2)))

%o (PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\2, (k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));

%Y Cf. A006154, A205571, A349104, A351937.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 26 2022