A207139 - OEIS

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

%S 1,2,7,147,14481,6183605,19196862399,206667738393577,

%T 6727813723143519624,1368162090055314881480420,

%U 1237384559488983889303951699285,3014186760620644058660289396656407831,34123084437870355957570087446546456971276065

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

%C The logarithmic derivative yields A207140.

%e G.f.: A(x) = 1 + 2*x + 7*x^2 + 147*x^3 + 14481*x^4 + 6183605*x^5 +...

%e where the logarithm of the g.f. equals the l.g.f. of A207140:

%e log(A(x)) = x + 2*x^2/2 + 10*x^3/3 + 407*x^4/4 + 56746*x^5/5 +...

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

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

%Y Cf. A207140 (log), A206850, A207135, A207137, A167006.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 15 2012