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 A206846 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2,k^2) * binomial(n^2,(n-k)^2) ). 2

%I #13 Mar 30 2012 18:37:35

%S 1,2,11,776,921193,10359730908,1620677532919905,

%T 1969126979596399128130,32593711828578589304123599877,

%U 3931730912701446701027876250509820962,6413805618092047206104426809813307222469463650,74040826359052943559114050244071546075856822107307951070

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

%C Logarithmic derivative yields A206847.

%e G.f.: A(x) = 1 + 2*x + 11*x^2 + 776*x^3 + 921193*x^4 + 10359730908*x^5 +...

%e where the logarithm of the g.f. yields the l.g.f. of A206847:

%e log(A(x)) = 2*x + 18*x^2/2 + 2270*x^3/3 + 3678482*x^4/4 + 51789416252*x^5/5 +...

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

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A206847 (log), A206848, A206850.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 15 2012

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