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G.f.: exp( Sum_{n>=1} A184731(n)*x^n/n ) where A184731(n) = Sum_{k=0..n} C(n,k)^(k+1).
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%I #15 Jan 10 2019 15:21:48

%S 1,2,5,20,159,3152,168036,20428850,5796209814,4052041564524,

%T 6210335115944263,21470958882165989854,183818137919395949397148,

%U 3517964195874870876682733562,147909303669340763210833833705995,15391220509661795085065182391703575606

%N G.f.: exp( Sum_{n>=1} A184731(n)*x^n/n ) where A184731(n) = Sum_{k=0..n} C(n,k)^(k+1).

%C Note that the following g.f. does NOT yield an integer series:

%C . exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^k] * x^n/n ).

%H Seiichi Manyama, <a href="/A184730/b184730.txt">Table of n, a(n) for n = 0..74</a>

%F Equals row sums of triangle A228899.

%F a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A184731(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Jan 10 2019

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 159*x^4 + 3152*x^5 +...

%e log(A(x)) = 2*x + 6*x^2/2 + 38*x^3/3 + 490*x^4/4 + 14152*x^5/5 + 969444*x^6/6 +...+ A184731(n)*x^n/n +...

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

%Y Cf. A184731, A181070, A228899.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 20 2011