OFFSET
0,3
COMMENTS
Compare to a g.f. for A000272: 1 = Sum_{n>=0} (n+1)^(n-1) * x^n/(1 + (n+1)*x)^(n+1).
FORMULA
a(n) = Sum_{k=1..n} -(-1)^k*binomial(2*n-k,k)*a(n-k)*(n-k+1)^k for n>=1 with a(0)=1.
EXAMPLE
G.f.: 1 = 1/(1+x) + x/(1+2*x)^3 + 5*x^2/(1+3*x)^5 + 52*x^3/(1+4*x)^7 + 860*x^4/(1+5*x)^9 + 19890*x^5/(1+6*x)^11 + 597113*x^6/(1+7*x)^13 +...
Compare to a g.f. for A000272:
1 = 1/(1+x) + x/(1+2*x)^2 + 3*x^2/(1+3*x)^3 + 4^2*x^3/(1+4*x)^4 + 5^3*x^4/(1+5*x)^5 + 6^4*x^5/(1+6*x)^6 + 7^5*x^6/(1+7*x)^7 +...
PROG
(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k/(1+(k+1)*x+x*O(x^n))^(2*k+1)), n)}
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, -(-1)^k*binomial(2*n-k, k)*a(n-k)*(n-k+1)^k))}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 17 2012
STATUS
approved