OFFSET
1,2
FORMULA
a(n) = n*Sum_{k=0..[n/2]} C(n-k,k)*C(2n-2k-1,n-k-1)^k/(n-k) for n>=1.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 676*x^5/5 +...
L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+10*x)^3*x^3/3 + (1+35*x)^4*x^4/4 +...
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 158*x^5 + 2474*x^6 +... (A159320).
MATHEMATICA
Table[n*Sum[Binomial[n-k, k]*Binomial[2n-2k-1, n-k-1]^k/(n-k), {k, 0, Floor[n/2]}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 06 2014 *)
PROG
(PARI) {a(n)=n*polcoeff(sum(m=1, n+1, (1+binomial(2*m-1, m-1)*x+x*O(x^n))^m*x^m/m), n)}
(PARI) {a(n)=n*sum(k=0, n\2, binomial(n-k, k)*binomial(2*n-2*k-1, n-k-1)^k/(n-k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 15 2009
STATUS
approved