A206155 - OEIS

%I #7 Mar 30 2012 18:37:35

%S 1,2,5,38,1425,283002,448468978,2707673843860,67018498701021670,

%T 14506787732148113566364,13603174532364904984495776225,

%U 43960529641219941452921634596223366,1207327102995668834632770987833295579308107,188859837731175560954429490131760211759694331013582

%N G.f.: exp( Sum_{n>=1} A206156(n)*x^n/n ), where A206156(n) = Sum_{k=0..n} binomial(n,k)^(2*k).

%C Logarithmic derivative yields A206156.

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 38*x^3 + 1425*x^4 + 283002*x^5 +...

%e where the logarithm of the g.f. begins:

%e log(A(x)) = 2*x + 6*x^2/2 + 92*x^3/3 + 5410*x^4/4 + 1400652*x^5/5 + 2687407464*x^6/6 +...+ A206156(n)*x^n/n +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,x^m/m*sum(k=0,m,binomial(m,k)^(2*k-0))+x*O(x^n))),n)}

%o for(n=0,16,print1(a(n),", "))

%Y Cf. A206156 (log), A184730, A206153, A206157, A206151.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2012