%I A138736
%S A138736 1,1,4,36,368,5200,90432,1884736,45817088,1273874688,39891461120,
%T A138736 1389816423424,53334303584256,2235679577657344,101651458028158976,
%U A138736 4983219643056537600,262026143585449607168,14711289584591513387008
%N A138736 Inverse binomial transform of A138737.
%C A138736 The n-th term of the n-th inverse binomial transform of A138737 equals 
               (n+1)^(n-1) for n>=0.
%C A138736 Related to LambertW(-x)/(-x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.
%F A138736 O.g.f. satisfies: [x^n] A( x/(1+(n-1)*x) )/(1+(n-1)*x) = (n+1)^(n-1) 
               for n>=0.
%F A138736 E.g.f. satisfies: [x^n] A(x)*exp(-(n-1)*x) = (n+1)^(n-1)/n! for n>=0.
%o A138736 (PARI) {a(n)=local(A=[1]);for(k=1,n,A=concat(A,0); A[k+1]=(k+1)^(k-1)-Vec(subst(Ser(A),
               x,x/(1+(k-1)*x+x*O(x^k)))/(1+(k-1)*x))[k+1]);A[n+1]}
%Y A138736 Cf. A138737.
%Y A138736 Sequence in context: A000765 A026334 A163455 this_sequence A019999 A002894 
               A131765
%Y A138736 Adjacent sequences: A138733 A138734 A138735 this_sequence A138737 A138738 
               A138739
%K A138736 nonn
%O A138736 0,3
%A A138736 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 05 2008