A180420 G.f. satisfies: A(A(x)) = x + A(2*x)^2.

1, 2, 12, 160, 4592, 276496, 34174592, 8570174016, 4335215019520, 4408454839564672, 8992935435667848448, 36753720073439398166016, 300717909357395506394597376, 4923649248081508021291300507648

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Formula

a(n)=T(n,1), T(n,m)=1/2*(kron_delta(n,m)+ sum(j=max(0,2*m-n)..m-1, binomial(m,j)*2^(n-j)*T(n-j,2*(m-j)))-sum(k=m+1..n-1, T(n,k)*T(k,m)))), n>m, T(n,n)=1. [Vladimir Kruchinin, May 03 2012]

Example

G.f.: A(x) = x + 2*x^2 + 12*x^3 + 160*x^4 + 4592*x^5 + 276496*x^6 +...
A(A(x)) = x + 4*x^2 + 32*x^3 + 448*x^4 + 11776*x^5 + 637952*x^6 +...
A(x)^2 = x^2 + 4*x^3 + 28*x^4 + 368*x^5 + 9968*x^6 + 575200*x^7 +...

Prog

(PARI) {a(n)=local(A=x+sum(k=2, n-1, a(k)*x^k)+x*O(x^n)); if(n==1, 1, polcoeff(x+subst(A, x, 2*x)^2-subst(A, x, A), n)/2)}
(Maxima) T(n, m):=( if n=m then 1 else 1/2*(kron_delta(n, m)+ sum(binomial(m, j)*2^(n-j)*T(n-j, 2*(m-j)), j, max(0, 2*m-n), m-1)-sum(T(n, k)*T(k, m), k, m+1, n-1))); makelist(T(n, 1), n, 1, 7); /* Vladimir Kruchinin, May 03 2012 */

Crossrefs

Sequence in context: A208577 A012646 A177778 * A012328 A302688 A201007

Adjacent sequences: A180417 A180418 A180419 * A180421 A180422 A180423

Keyword

nonn

Author

Paul D. Hanna, Sep 03 2010

Status

approved