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A143598 E.g.f.: A(x) = exp(x*sinh(x*G(x))) where G(x) = cosh(x*G(x)) is the e.g.f. of A143601.

%I A143598 #2 Mar 30 2012 18:37:11
%S A143598 1,2,28,1176,103440,15726880,3684098496,1232799974784,558670427013376,
%T A143598 329559835063067136,245462725323910487040,225319148634038399801344,
%U A143598 249936012383478860884217856,329609037187846742271984869376
%N A143598 E.g.f.: A(x) = exp(x*sinh(x*G(x))) where G(x) = cosh(x*G(x)) is the e.g.f. of A143601.
%F A143598 E.g.f.: A(x) = exp(x*F(x)) where F(x) is the e.g.f. of A007106.
%F A143598 E.g.f.: A(x) = sqrt(H(x)*H(-x)) where H(x) = exp(x*sqrt(H(x)/H(-x))) is the e.g.f. of A143599.
%F A143598 E.g.f. satisfies: A(x/cosh(x)) = exp(x*tanh(x)). [From _Paul D. Hanna_, Aug 29 2008]
%e A143598 E.g.f.: A(x) = 1 + 2*x^2/2! + 28*x^4/4! + 1176*x^6/6! + 103440*x^8/8! +...
%e A143598 A(x) = exp(x*F(x)) where F(x) = e.g.f. of A007106:
%e A143598 F(x) = x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + 686080*x^9/9! +...
%e A143598 A(x) = exp(x*sqrt(G(x)^2 - 1)) where G(x) = e.g.f. of A143601:
%e A143598 G(x) = 1 + x^2/2! + 13*x^4/4! + 541*x^6/6! + 47545*x^8/8! +...
%e A143598 A(x) = sqrt(H(x)*H(-x)) where H(x) = e.g.f. of A143599:
%e A143598 H(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 53*x^4/4! + 316*x^5/5! +...
%o A143598 (PARI) {a(n)=local(G=1+x*O(x^n));for(i=0,n,G=cosh(x*G));n!*polcoeff(exp(x*sqrt(G^2-1)),n)}
%Y A143598 Cf. A058014, A143600, A143601, A007106.
%K A143598 nonn
%O A143598 0,2
%A A143598 _Paul D. Hanna_, Aug 27 2008