A209625 G.f. A(x) satisfies A(A(x)-2*A(x)^2)=x/(1-2*x)

1, 2, 6, 24, 114, 600, 3372, 19824, 120422, 749848, 4760228, 30688560, 200338740, 1321408656, 8791205496, 58912586784, 397228820742, 2692522813848, 18333530047428, 125325068538672, 859639878194844

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

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

Prog

(Maxima)
T(n, m):=if n=m then 1 else 1/2*(binomial(n-1, m-1)*2^(n-m)-(sum(T(k, m)*sum(T(n, i)*binomial(k, i-k)*(-2)^(i-k), i, k, n), k, m+1, n-1)+sum(T(n, i)*binomial(m, i-m)*(-2)^(i-m), i, m+1, n)));
makelist(T(n, 1), n, 1, 7);

Crossrefs

Sequence in context: A192088 A245233 A228907 * A054872 A134664 A375913

Adjacent sequences: A209622 A209623 A209624 * A209626 A209627 A209628

Keyword

nonn

Author

Vladimir Kruchinin, Mar 11 2012

Status

approved