A362166 - OEIS

%I #11 Dec 04 2023 06:19:16

%S 1,-1,3,-1,41,299,4531,74507,1474481,33540119,864507491,24891022199,

%T 791755864153,27571976573699,1043247441846611,42615848603499779,

%U 1869129393654945761,87605345727468933167,4369604246576366377411,231091472431638655755119

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

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

%F D-finite with recurrence +(-9*n+11)*a(n) +2*(27*n^2-121*n+72)*a(n-1) +3*(-27*n^3+304*n^2-1053*n+1056)*a(n-2) +(-612*n^3+6984*n^2-23677*n+21227) *a(n-3) +4*(27*n-23)*(n-3)*a(n-4) -48*(9*n-10) *(n-3)*(n-4) *a(n-5) +64*(n-5)*(n-4)*(9*n^2-62*n+78)*a(n-6) +256*(n-5) *(n-6)*(17*n-24)*(n-4)*a(n-7)=0. - _R. J. Mathar_, Dec 04 2023

%p A362166 := proc(n)

%p     (-1)^n*n!*add(3^k * binomial((n-k)/3,k)/(n-k)!,k=0..n) ;

%p end proc:

%p seq(A362166(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023

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

%Y Cf. A362162, A362164.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Apr 10 2023