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A162650 E.g.f. satisfies: A(x) = exp( sinh(x*A(x)) ).

%I A162650 #6 Jul 15 2014 12:18:51
%S A162650 1,1,3,17,145,1657,23779,411329,8335233,193742001,5082443619,
%T A162650 148557955537,4788293136081,168731904680809,6453754733373315,
%U A162650 266292315945201409,11790632930559453313,557631368540974947169
%N A162650 E.g.f. satisfies: A(x) = exp( sinh(x*A(x)) ).
%H A162650 Vaclav Kotesovec, <a href="/A162650/b162650.txt">Table of n, a(n) for n = 0..370</a>
%F A162650 a(n) = Sum_{k=0..n} (n+1)^(k-1)/k! * Sum_{j=0..k} C(k,j)*(2j-k)^n/2^k.
%F A162650 Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then
%F A162650 a(n,m) = Sum_{k=0..n} m*(n+m)^(k-1)/k! * Sum_{j=0..k} C(k,j)*(2j-k)^n/2^k.
%F A162650 a(n) ~ n^(n-1) / (sqrt(1/s^2+r^2*log(s)) * exp(n) * r^n), where r = 0.3296546568511367672... and s = 2.320640520774412031... are roots of the system of equations sinh(r*s) = log(s), r*s*cosh(r*s) = 1. - _Vaclav Kotesovec_, Jul 15 2014
%e A162650 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 17*x^3/3! + 145*x^4/4! + 1657*x^5/5! +...
%e A162650 log(A(x)) = sinh(x*A(x)) where
%e A162650 log(A(x)) = x + 2*x^2/2! + 10*x^3/3! + 80*x^4/4! + 876*x^5/5! + 12192*x^6/6! +...
%o A162650 (PARI) {a(n,m=1)=sum(k=0,n,m*(n+m)^(k-1)/k!*sum(j=0,k,(-1)^(k-j)*binomial(k,j)*(2*j-k)^n/2^k))}
%Y A162650 Cf. A162649.
%K A162650 nonn
%O A162650 0,3
%A A162650 _Paul D. Hanna_, Jul 08 2009