%I #20 Mar 01 2024 02:04:58
%S 1,1,3,6,21,51,201,498,2241,4581,26991,17766,359613,-995409,6968781,
%T -53627454,259953921,-2292378327,13839388731,-108459180954,
%U 809434284741,-6158416812309,50614251147153,-407335408369614,3478999597913601,-30042633320442099,266107969086122151
%N Expansion of e.g.f. exp(x+x^2-1/6*x^3).
%F a(n) = n!*sum(k=0..n, sum(j=0..k, binomial(j,n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k,j))/k!).
%F D-finite with recurrence 2*a(n) -2*a(n-1) +4*(-n+1)*a(n-2) +(n-1)*(n-2)*a(n-3)=0. - _Bruno Berselli_, Nov 17 2011
%o (Maxima) a(n):=n!*sum(sum(binomial(j,n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k,j),j,0,k)/k!,k,0,n);
%K sign
%O 0,3
%A _Vladimir Kruchinin_, Nov 17 2011