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A228905 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) * x^k ).

%I A228905 #5 Nov 06 2014 08:25:42
%S A228905 1,1,2,3,5,12,33,139,1251,10598,176642,4720781,106779821,5953841083,
%T A228905 373265833332,23827795512789,3914313805097976,548326897932632059,
%U A228905 108647952177920032693,45931050219457726501030,14741338951262398648743248,9489791738688118291360645939
%N A228905 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) * x^k ).
%C A228905 Equals the antidiagonal sums of triangle A228904.
%H A228905 Vaclav Kotesovec, <a href="/A228905/b228905.txt">Table of n, a(n) for n = 0..120</a>
%e A228905 G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 12*x^5 + 33*x^6 + 139*x^7 +...
%e A228905 such that, by definition, the logarithm equals (cf. A228832):
%e A228905 log(A(x)) = (1 + x)*x + (1 + 2*x + x^2)*x^2/2 + (1 + 3*x + 15*x^2 + x^3)*x^3/3 + (1 + 4*x + 70*x^2 + 220*x^3 + x^4)*x^4/4 + (1 + 5*x + 210*x^2 + 5005*x^3 + 4845*x^4 + x^5)*x^5/5 +...
%e A228905 More explicitly,
%e A228905 log(A(x)) = x + 3*x^2/2 + 4*x^3/3 + 7*x^4/4 + 31*x^5/5 + 114*x^6/6 + 687*x^7/7 + 8679*x^8/8 + 82948*x^9/9 +...
%o A228905 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m*k, k^2)*x^k)*x^m/m)+x*O(x^n)), n)}
%o A228905 for(n=0, 25, print1(a(n), ", "))
%Y A228905 Cf. A228904, A228832.
%Y A228905 Cf. variants: A206850, A207137, A206830.
%K A228905 nonn
%O A228905 0,3
%A A228905 _Paul D. Hanna_, Sep 07 2013