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A228809 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) ).

%I A228809 #14 Jan 19 2019 07:03:51
%S A228809 1,2,4,12,94,2195,158904,31681195,13904396167,15305894726347,
%T A228809 44888344014554903,288228807835914177564,4270880356112396772814732,
%U A228809 169380654509201278629725097906,15394658527137259981745081997280638,3042352591056504014301304188228238554499
%N A228809 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) ).
%C A228809 Logarithmic derivative equals A228808.
%C A228809 Equals row sums of triangle A228904.
%H A228809 Seiichi Manyama, <a href="/A228809/b228809.txt">Table of n, a(n) for n = 0..73</a>
%e A228809 G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 94*x^4 + 2195*x^5 +...
%e A228809 where
%e A228809 log(A(x)) = 2*x + 4*x^2/2 + 20*x^3/3 + 296*x^4/4 + 10067*x^5/5 + 927100*x^6/6 +...+ A228808(n)*x^n/n +...
%o A228809 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, x^m/m*sum(k=0, m, binomial(m*k, k^2)))+x*O(x^n)), n)}
%o A228809 for(n=0, 20, print1(a(n), ", "))
%Y A228809 Cf. A228808, A207135, A228904.
%Y A228809 Cf. variants: A167006, A206848.
%K A228809 nonn
%O A228809 0,2
%A A228809 _Paul D. Hanna_, Sep 04 2013