OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n-1} 2^k*(n-k)^k * a(k) for n>0 with a(0)=1.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 191*x^4 + 4261*x^5 +...
where:
A(x) = 1 + x*A(2*x) + x^2*A(4*x) + x^3*A(6*x) + x^4*A(8*x) + x^5*A(10*x) +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*subst(A, x, 2*j*x))); polcoeff(A, n)}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, 2^k*(n-k)^k*a(k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 08 2011
STATUS
approved