%I A143805
%S A143805 1,1,2,7,36,250,2229,24656,329883,5233837,96907908,2066551242,
%T A143805 50196458429,1375782397859,42203985613593,1438854199059479,
%U A143805 54180508061067099,2241000820010271224,101316373253530824771
%N A143805 Eigensequence of triangle A130534.
%C A143805 1;
%C A143805 1, 1;
%C A143805 2, 3, 1;
%C A143805 6, 11, 6, 1;
%C A143805 24, 50, 35, 10, 1;
%C A143805 ...
%C A143805 Shift the entire triangle down 1 place, with T(0,0) = 1. Let T = the 
               new triangle: (1; 1; 1, 1; 2, 3, 1;...).
%C A143805 Sequence A143805 = Lim_{n -> inf.} T^n as a vector.
%F A143805 Given triangle A130534:
%F A143805 E.g.f.: Sum_{n>=0} a(n)*x^n/n! = 1 + Sum_{n>=1} a(n-1)*(-log(1-x))^n/
               n!. [From Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009]
%e A143805 Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009: 
               (Start)
%e A143805 E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 36*x^4/4! + 250*x^5/5! +...
%e A143805 A(x) = 1 - log(1-x) + log(1-x)^2/2! - 2*log(1-x)^3/3! + 7*log(1-x)^4/
               4! - 36*log(1-x)^5/5! +-... (End)
%o A143805 (PARI) {a(n)=local(A=[1]);for(i=1,n,A=Vec(serlaplace(1+sum(k=1,#A,A[k]*(-log(1-x+x*O(x^n)))^k/
               k!))));A[n+1]} [From Paul D. Hanna (pauldhanna(AT)juno.com), May 
               20 2009]
%Y A143805 A143806
%Y A143805 Sequence in context: A007889 A125033 A034430 this_sequence A112293 A090352 
               A123549
%Y A143805 Adjacent sequences: A143802 A143803 A143804 this_sequence A143806 A143807 
               A143808
%K A143805 nonn
%O A143805 1,3
%A A143805 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008
%E A143805 Extended by Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009