A351930 - OEIS

%I #20 Mar 09 2022 06:21:49

%S 1,1,1,1,0,-4,-14,-34,-34,190,1366,5446,11056,-30744,-421420,-2403764,

%T -7434244,9782396,296347996,2257819420,9461601856,-1690329584,

%U -395833164264,-3872875071064,-20629371958040,-17208144880024,893208132927176,10962683317693576

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

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

%F D-finite with recurrence a(n) = a(n-1) - binomial(n-1,3) * a(n-4) for n > 3.

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

%p      `if`(n<4, 0, -a(n-4)*binomial(n-1, 3))+a(n-1))

%p     end:

%p seq(a(n), n=0..27);  # _Alois P. Heinz_, Feb 26 2022

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

%o (PARI) a(n) = n!*sum(k=0, n\4, (-1/4!)^k*binomial(n-3*k, k)/(n-3*k)!);

%o (PARI) a(n) = if(n<4, 1, a(n-1)-binomial(n-1, 3)*a(n-4));

%Y Cf. A351929, A351931.

%Y Cf. A351905, A351932.

%K sign

%O 0,6

%A _Seiichi Manyama_, Feb 26 2022