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Expansion of e.g.f. exp(x+x^2-1/6*x^3).
0

%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