A352327 - OEIS

%I #19 Mar 25 2022 10:18:21

%S 1,1,4,19,130,1081,10894,127639,1711210,25798141,432212134,7964801659,

%T 160121522290,3487254825601,81790592435374,2055350489070079,

%U 55093108433421370,1569052795651631461,47315282424232826614,1506074331671551028899

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

%H Seiichi Manyama, <a href="/A352327/b352327.txt">Table of n, a(n) for n = 0..414</a>

%F a(0) = 1; a(n) = Sum_{k=1..n} (3+(-1)^k)/2 * binomial(n,k) * a(n-k).

%F a(n) ~ n! / (sqrt(6) * log(1 + sqrt(2/3))^(n+1)). - _Vaclav Kotesovec_, Mar 12 2022

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p       a(n-k)*binomial(n, k)*(2-(k mod 2)), k=1..n))

%p     end:

%p seq(a(n), n=0..19); # _Alois P. Heinz_, Mar 25 2022

%t m = 19; Range[0, m]! * CoefficientList[Series[1/(3 - Exp[x] - Cosh[x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(x)-cosh(x))))

%o (PARI) a(n) = if(n==0, 1, sum(k=1, n, (3+(-1)^k)/2*binomial(n, k)*a(n-k)));

%Y Cf. A000670, A006154, A094088, A352326, A352624.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 12 2022