0,3

E.g.f.: A(x) = exp(x + x^2*A(x)). [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2008]

Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Jun 17 2009: (Start)

a(n) = Sum_{k=0..n} n! * (n-k+1)^(k-1)/k! * C(k,n-k).

Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then

a(n,m) = Sum_{k=0..n} n! * m*(n-k+m)^(k-1)/k! * C(k,n-k). (End)

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 85*x^4/4! + 701*x^5/5! +... [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2008]

(PARI) {a(n)=local(Ex=exp(x+x*O(x^n)), W=Ex); for(k=0, n, W=exp(x*W)); n!*polcoeff(subst(W, x, x^2*Ex)*Ex, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2007

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=exp(x+x^2*A)); n!*polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2008]

Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Jun 17 2009: (Start)

(PARI) {a(n, m=1)=if(n==0, 1, sum(k=0, n, n!/k!*m*(n-k+m)^(k-1)*binomial(k, n-k)))}

(PARI) {a(n, m=1)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(x*(1+x*A))); n!*polcoeff(A^m, n)} (End)

Sequence in context: A104032 A130406 A152789 this_sequence A121679 A023037 A157451

Adjacent sequences: A125497 A125498 A125499 this_sequence A125501 A125502 A125503

easy,nonn

Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2006

More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2007