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%I #10 Feb 19 2015 15:57:22
%S 1,1,3,18,213,4128,122638,5096305,284192429,20375905738,1829560187405,
%T 200829815300994,26471873341135571,4124649654997542447,
%U 750006492020987263020,157382918361825037892997
%N G.f.: A(x) = exp( Sum_{n>=1} A183240(n)*x^n/n ) where A183240 is the sums of the squares of multinomial coefficients.
%C Conjectured to consist entirely of integers.
%H Vaclav Kotesovec, <a href="/A183241/b183241.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = (1/n)*Sum_{k=1..n} A183240(k)*a(n-k) for n>0 with a(0)=1.
%F a(n) ~ c * n! * (n-1)!, where c = Product_{k>=2} 1/(1-1/(k!)^2) = 1.37391178018464563291... . - _Vaclav Kotesovec_, Feb 19 2015
%e G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 213*x^4 + 4128*x^5 +...
%e log(A(x)) = x + 5*x^2/2 + 46*x^3/3 + 773*x^4/4 + 19426*x^5/5 + 708062*x^6/6 + 34740805*x^7/7 +...+ A183240(n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(intformal(1/x*(-1+serlaplace(serlaplace(1/prod(k=1,n+1,1-x^k/k!^2+O(x^(n+2)))))))),n)}
%Y Cf. A183240, A183239.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 04 2011
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