%I A156325
%S A156325 1,1,4,34,482,10056,286372,10591372,491169996,27826318000,1887581200256,
%T A156325 150885500428224,14028718134958936,1500672248541122944,
%U A156325 182987661921689610000,25231215606822797450176
%N A156325 E.g.f.: A(x) = exp( Sum_{n>=1} n(n+1)/2 * a(n-1)*x^n/n! ) = Sum_{n>=0} 
               a(n)*x^n/n! with a(0)=1.
%F A156325 a(n) = Sum_{k=1..n} k(k+1)/2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with 
               a(0)=1.
%e A156325 E.g.f: A(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 482*x^4/4! + 10056*x^5/5! 
               +...
%e A156325 log(A(x)) = x + 3*1*x^2/2! + 6*4*x^3/3! + 10*34*x^4/4! + 15*482*x^5/5! 
               +...
%o A156325 (PARI) {a(n)=if(n==0,1,n!*polcoeff(exp(sum(k=1,n,k*(k+1)/2*a(k-1)*x^k/
               k!)+x*O(x^n)),n))}
%o A156325 (PARI) {a(n)=if(n==0,1,sum(k=1,n,k*(k+1)/2*binomial(n-1,k-1)*a(k-1)*a(n-k)))}
%Y A156325 Cf. A156326, A156327.
%Y A156325 Sequence in context: A071213 A052629 A151919 this_sequence A111169 A002105 
               A081972
%Y A156325 Adjacent sequences: A156322 A156323 A156324 this_sequence A156326 A156327 
               A156328
%K A156325 nonn
%O A156325 0,3
%A A156325 Paul D. Hanna (pauldhanna(AT)juno.com), Feb 08 2009