A228852 - OEIS

%I #5 Sep 05 2013 12:46:43

%S 1,1,2,14,382,38344,12990279,14369538529,50897796053428,

%T 572602411324905786,20308462423438736818782,

%U 2261760763404526386241849803,788248543938180828988762846368690,857323841081698966408121705146996762240,2905542652088907570108828021890682181041282730

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

%C Self-convolution yields A207135.

%e G.f.: A(x) = 1 + x + 2*x^2 + 14*x^3 + 382*x^4 + 38344*x^5 + 12990279*x^6 +...

%e where

%e log(A(x)) = x + 3*x^2/2 + 37*x^3/3 + 1471*x^4/4 + 189751*x^5/5 + 77708973*x^6/6 +...+ A207136(n)/2 * x^n/n +...

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

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A207135, A207136.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 05 2013