%I #19 Jan 19 2019 07:03:33

%S 1,2,6,66,4258,1337374,1933082159,11353941470188,291885138650054688,

%T 29463501750534915665304,12844314786465829040693498639,

%U 21675661852919288704454219459892060,156969579902607123047763327413679853875703

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

%C Logarithmic derivative yields A167009.

%C Equals row sums of triangle A209196.

%H Seiichi Manyama, <a href="/A167006/b167006.txt">Table of n, a(n) for n = 0..57</a>

%e G.f.: A(x) = 1 + 2*x + 6*x^2 + 66*x^3 + 4258*x^4 + 1337374*x^5 +...

%e log(A(x)) = 2*x + 8*x^2/2 + 170*x^3/3 + 16512*x^4/4 + 6643782*x^5/5 + 11582386286*x^6/6 +...+ A167009(n)*x^n/n +...

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

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

%Y Cf. A167009, A209196, A155200.

%Y Cf. variants: A206848, A228809.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 17 2009