A351935 - OEIS

%I #19 Jun 08 2024 08:51:49

%S 1,1,1,1,1,6,31,106,281,1261,10711,71611,350461,1808236,17037021,

%T 170285116,1293714241,8653175441,84433291741,1063629264781,

%U 11218379358721,97926941650546,1021280770603171,14623420493573046,197153396050112041,2190425085571083901

%N Expansion of e.g.f. exp(x / (1 - x^4/24)).

%F a(n) = Sum_{k=0..floor((n-1)/4)} (4*k+1)!/24^k * binomial(n-1,4*k) * a(n-1-4*k) for n > 4.

%F a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k)/(24^k * (n-4*k)!). - _Seiichi Manyama_, Jun 08 2024

%t m = 25; Range[0, m]! * CoefficientList[Series[Exp[x/(1 - x^4/24)], {x, 0, m}], x] (* _Amiram Eldar_, Feb 26 2022 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x^4/24))))

%o (PARI) a(n) = if(n<5, 1, sum(k=0, (n-1)\4, (4*k+1)!/24^k*binomial(n-1, 4*k)*a(n-1-4*k)));

%Y Cf. A000262, A351933, A351934, A351936.

%Y Cf. A275423.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Feb 26 2022