cp's OEIS Frontend

A371456 Expansion of 1/(1 - x/(1 - 9*x^2)^(1/3)).

%I A371456 #27 Jun 11 2024 08:30:54
%S A371456 1,1,1,4,7,28,58,223,505,1876,4498,16255,40576,143422,368965,1280830,
%T A371456 3373225,11536309,30958240,104559082,284934754,952183048,2628211291,
%U A371456 8703329266,24283705558,79785964555,224677646416,733160045533,2081054132179,6750196280983
%N A371456 Expansion of 1/(1 - x/(1 - 9*x^2)^(1/3)).
%F A371456 a(n) = Sum_{k=0..floor(n/2)} 9^k * binomial((n+k)/3-1,k).
%F A371456 D-finite with recurrence -(n-1)*(n-2)*(n-8)*a(n) +3*(9*n^3-123*n^2+490*n-616)*a(n-2) +(n-1)*(n-2)*(n-8)*a(n-3) +9*(-27*n^3+441*n^2-2318*n+3984)*a(n-4) +6*(-3*n^3+45*n^2-206*n+284)*a(n-5) +81*(3*n-20)*(n-6)*(3*n-19)*a(n-6) +9*(3*n-20)*(n-6)*(3*n-19)*a(n-7)=0. - _R. J. Mathar_, Jun 07 2024
%F A371456 a(n) == 1 (mod 3). - _Seiichi Manyama_, Jun 11 2024
%p A371456 A371456 := proc(n)
%p A371456     add(9^k*binomial((n+k)/3-1,k),k=0..floor(n/2)) ;
%p A371456 end proc:
%p A371456 seq(A371456(n),n=0..70) ; # _R. J. Mathar_, Jun 07 2024
%o A371456 (PARI) a(n) = sum(k=0, n\2, 9^k*binomial((n+k)/3-1, k));
%Y A371456 Cf. A362206, A371458.
%Y A371456 Cf. A373543.
%K A371456 nonn
%O A371456 0,4
%A A371456 _Seiichi Manyama_, Jun 07 2024