A209627 E.g.f. satisfies A(A(x)*exp(-2*A(x)))=x

1, 2, 12, 124, 1820, 34476, 796600, 21647088, 674894736, 23727325600, 929120132336, 40145865303072, 1899037891380448, 97624128373666272, 5416162739385169920, 322369745413410839296, 20496143199154076929280

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

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

Example

E.g.f: A(x) = x + 2*x^2/2! + 12*x^3/3! + 124*x^4/4! + 1820*x^5/5! +...
where
A(A(x)) = x + 4*x^2/2! + 36*x^3/3! + 512*x^4/4! + 10000*x^5/5! +...+ (2*n)^(n-1)*x^n/n! +...

Prog

(Maxima)
T(n, m):=if n=m then 1 else -1/2*(sum(T(k, m)*sum(T(n, i)*(k^(i-k)*(-2)^(i-k))/(i-k)!, i, k, n), k, m+1, n-1)+sum(T(n, i)*(m^(i-m)*(-2)^(i-m))/(i-m)!, i, m+1, n));
makelist(n!*T(n, 1), n, 1, 7);
(PARI) {a(n)=local(W=sum(m=1, n, (2*m)^(m-1)*x^m/m!)+x*O(x^n), A=x);
for(i=1, n, A=(A+subst(W, x, serreverse(A+x*O(x^n))))/2); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", ")) \\ Paul D. Hanna, May 28 2013

Crossrefs

Sequence in context: A173219 A227458 A035351 * A253282 A201470 A349268

Adjacent sequences: A209624 A209625 A209626 * A209628 A209629 A209630

Keyword

nonn

Author

Vladimir Kruchinin, Mar 11 2012

Status

approved