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A159312 Logarithm derivative of the g.f. of A159311 such that a(n) = (n-1)*A159311(n) + 1.

%I A159312 #2 Mar 30 2012 18:37:17
%S A159312 1,3,13,79,601,5331,53173,584543,6994417,90319843,1250828701,
%T A159312 18488472751,290534988745,4837973367475,85124614459333,
%U A159312 1578579744746431,30781661041632481,629806296977373891,13494417486970553389
%N A159312 Logarithm derivative of the g.f. of A159311 such that a(n) = (n-1)*A159311(n) + 1.
%e A159312 L.g.f.: L(x) = x + 3*x^2/2 + 13*x^3/3 + 79*x^4/4 + 601*x^5/5 + 5331*x^6/2 +...
%e A159312 exp(L(x)) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 150*x^5 + 1066*x^6 +...
%e A159312 exp(L(x)) is the g.f. of A159311 where a(n) = (n-1)*A159311(n) + 1:
%e A159312 3 = 1*2 + 1, 13 = 2*6 + 1, 79 = 3*26 + 1, 601 = 4*15 + 1, 5331 = 5*1066 + 1.
%o A159312 (PARI) {a(n)=local(G003319=1-1/sum(k=0,n+1,k!*x^k+x^2*O(x^n)));n*polcoeff(log(x/serreverse(G003319)),n)}
%Y A159312 Cf. A159311.
%K A159312 nonn
%O A159312 1,2
%A A159312 _Paul D. Hanna_, Apr 16 2009