A207135 - OEIS

%I #10 Sep 07 2013 20:33:38

%S 1,2,5,32,796,77508,26058970,28765221688,101824384364586,

%T 1145306676113095172,40618070255705049577152,

%U 4523562146025746408072408406,1576501611479138389748204925102907,1714649258669533421310212170714443813118

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

%C The logarithmic derivative yields A207136.

%C Equals the row sums of triangle A228900.

%C Equals the self-convolution of A228852.

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 32*x^3 + 796*x^4 + 77508*x^5 +...

%e where the logarithm of the g.f. equals the l.g.f. of A207136:

%e log(A(x)) = 2*x + 6*x^2/2 + 74*x^3/3 + 2942*x^4/4 + 379502*x^5/5 +...

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

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

%Y Cf. A207136 (log), A167006, A228900, A206830, A206850, A228852.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 15 2012