A220288 G.f. A(x) satisfies A(A(A(x)))=(x+3*x^2+9*x^3).

1, 1, 1, -8, 28, -26, -386, 2701, -5399, -42155, 358615, -354212, -10419524, 52825312, 236952352, -3103798967, -3013742105, 176201013745, -164790760103, -11763898514324, 27830312919316, 992172068848126, -3681957974446718, -103284064687144985, 528045230825074855

Offset

1,4

Links

Table of n, a(n) for n=1..25.

Formula

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.

Mathematica

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 *)

Prog

(Maxima)
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));
makelist(T(n, 1), n, 1, 7);

Crossrefs

Sequence in context: A053619 A272259 A112663 * A201101 A201105 A184614

Adjacent sequences: A220285 A220286 A220287 * A220289 A220290 A220291

Keyword

sign

Author

Dmitry Kruchinin, Dec 09 2012

Status

approved