A201778 G.f. satisfies A(x/(1-x)) = x*(1-sqrt(1-4*A(x)))/(2*A(x)).

1, 0, 1, 2, 5, 14, 39, 110, 323, 956, 2835, 8648, 26449, 80356, 253709, 789110, 2400681, 8095578, 24339611, 71349218, 314555855, 559848480, 2096495479, 23012907844, -84278218251, 415921423864, 2974067144745

Offset

1,4

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = T(n,1), T(n,m) = Sum_{k=1..n-m} T(n-m,k)*m*binomial(2*k+m-1,k+m-1)/(k+m)-binomial(n-1,k+m-2)*T(k+m-1,m), n>m, T(n,n)=1.

Prog

(Maxima)
array(BB, 100, 100);
fillarray (BB, makelist (-1, i, 1, 1000));
T(n, m):=if BB[n, m]=-1 then BB[n, m]:(if n=m then 1 else sum(T(n-m, k)*m*binomial(2*k+m-1, k+m-1)/(k+m)-binomial(n-1, k+m-2)*T(k+m-1, m), k, 1, n-m)) else BB[n, m];
makelist(T(n, 1), n, 1, 27);

Crossrefs

Sequence in context: A000641 A368672 A026135 * A367655 A105641 A027035

Adjacent sequences: A201775 A201776 A201777 * A201779 A201780 A201781

Keyword

sign

Author

Vladimir Kruchinin, Dec 04 2011

Status

approved