|
%I #12 Mar 12 2022 11:15:07
%S 1,1,3,13,76,551,4803,48833,567465,7418263,107752293,1721642143,
%T 30008756055,566650322031,11523037802461,251062618129063,
%U 5834798259848815,144078299659541361,3766993649599221903,103961442644871088897,3020133228180079209075
%N Expansion of e.g.f. 1/(2 - exp(x) - x^4/24).
%F a(n) = binomial(n,4) * a(n-4) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.
%t m = 20; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^4/24), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^4/24)))
%o (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m))*binomial(n, k)*b(n-k, m)));
%o a(n) = b(n, 4);
%Y Cf. A006155, A352306, A352307.
%Y Cf. A352300.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 11 2022
|
