OFFSET
0,3
FORMULA
a(n) = (-1)^n * n! * Sum_{k=0..n} 3^k * binomial((n-k)/3,k)/(n-k)!.
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
MAPLE
A362166 := proc(n)
(-1)^n*n!*add(3^k * binomial((n-k)/3, k)/(n-k)!, k=0..n) ;
end proc:
seq(A362166(n), n=0..70) ; # R. J. Mathar, Dec 04 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-3*x)^(1/3))))
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Apr 10 2023
STATUS
approved