A206151 - OEIS

%I #11 Dec 30 2012 11:17:22

%S 1,2,7,120,16257,22426576,181974299842,15238138790731690,

%T 8413234043413844801094,36597622942948070873495055416,

%U 1557743574279376981523155294991683637,377269728353963189455845962558983304322979834

%N G.f.: exp( Sum_{n>=1} A206152(n)*x^n/n ), where A206152(n) = Sum_{k=0..n} binomial(n,k)^(n+k).

%C Logarithmic derivative yields A206152.

%e G.f.: A(x) = 1 + 2*x + 7*x^2 + 120*x^3 + 16257*x^4 + 22426576*x^5 +...

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

%e log(A(x)) = 2*x + 10*x^2/2 + 326*x^3/3 + 64066*x^4/4 + 111968752*x^5/5 +...+ A206152(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)^(m+k))+x*O(x^n))),n)}

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

%Y Cf. A206152 (log), A184730.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2012