A220288 - OEIS

%I #16 May 04 2024 09:23:27

%S 1,1,1,-8,28,-26,-386,2701,-5399,-42155,358615,-354212,-10419524,

%T 52825312,236952352,-3103798967,-3013742105,176201013745,

%U -164790760103,-11763898514324,27830312919316,992172068848126,-3681957974446718,-103284064687144985,528045230825074855

%N G.f. A(x) satisfies A(A(A(x))) = x+3*x^2+9*x^3.

%H Seiichi Manyama, <a href="/A220288/b220288.txt">Table of n, a(n) for n = 1..200</a>

%F a(n)=T(n,1), T(n, m)=1/3*(3^(n-m)*sum(j=0..m, binomial(j,n-3*m+2*j)*binomial(m,j))-sum(k=m+1..n-1, T(k, m)*sum(, i=k..n, T(n, i)*T(i, k)))-sum(i=m+1..n-1, T(n, i)*T(i, m))), T(n,n)=1.

%t t[n_, m_] := t[n, m] = 1/3*(3^(n - m)* Sum[Binomial[j, n - 3*m + 2*j]*Binomial[m, j], {j, 0, m}] - Sum[t[k, m]*Sum[t[n, i]*t[i, k], {i, k, n}], {k, m + 1, n - 1}] - Sum[t[n, i]*t[i, m], {i, m + 1, n - 1}]); t[n_, n_] = 1; Table[t[n, 1], {n, 1, 25}] (* _Jean-François Alcover_, Feb 22 2013 *)

%o (Maxima)

%o T(n, m):=if n=m then 1 else 1/3*(3^(n-m)*sum(binomial(j,n-3*m+2*j)*binomial(m,j),j,0,m)-sum(T(k, m)*sum(T(n, i)*T(i, k), i, k, n), k, m+1, n-1)-sum(T(n, i)*T(i, m), i, m+1, n-1));

%o makelist(T(n,1),n,1,7);

%Y C. A141118, A220110.

%K sign

%O 1,4

%A _Dmitry Kruchinin_, Dec 09 2012