|
%I #9 Apr 22 2024 12:40:25
%S 1,3,-6,36,-216,1404,-9648,68904,-506304,3802464,-29055024,225142416,
%T -1764900576,13970400480,-111506362560,896391836928,-7251109424640,
%U 58978357310592,-482049643011840,3957079727715840,-32609916223598592,269682253882186752
%N G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + x*A(x)) )^(1/3).
%F a(n) = Sum_{k=0..n} 9^k * binomial(n/3-k/3+1/3,k) * binomial(k,n-k)/(n-k+1).
%F D-finite with recurrence n*(n-2)*a(n) +3*(8*n^2-31*n+24)*a(n-1) +27*(7*n^2-41*n+56)*a(n-2) +54*(3*n-10)*(3*n-14)*a(n-3) -108*(n-4)*(n-7)*a(n-6) -648*(n-6)*(n-8)*a(n-7)=0. - _R. J. Mathar_, Apr 22 2024
%p A372003 := proc(n)
%p add(9^k*binomial((n-k+1)/3,k)*binomial(k,n-k)/(n-k+1),k=0..n) ;
%p end proc:
%p seq(A372003(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o (PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3-k/3+1/3, k)*binomial(k, n-k)/(n-k+1));
%Y Cf. A372002.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 15 2024
|
