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.

1, 2, 28, 1176, 103440, 15726880, 3684098496, 1232799974784, 558670427013376, 329559835063067136, 245462725323910487040, 225319148634038399801344, 249936012383478860884217856, 329609037187846742271984869376

Offset: 0

Author

Paul D. Hanna, Aug 27 2008

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x^2/2! + 28*x^4/4! + 1176*x^6/6! + 103440*x^8/8! +...
A(x) = exp(x*F(x)) where F(x) = e.g.f. of A007106:
F(x) = x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + 686080*x^9/9! +...
A(x) = exp(x*sqrt(G(x)^2 - 1)) where G(x) = e.g.f. of A143601:
G(x) = 1 + x^2/2! + 13*x^4/4! + 541*x^6/6! + 47545*x^8/8! +...
A(x) = sqrt(H(x)*H(-x)) where H(x) = e.g.f. of A143599:
H(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 53*x^4/4! + 316*x^5/5! +...
		

Crossrefs

Cf. A058014, A143600, A143601, A007106.

Programs

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)}

Formula

E.g.f.: A(x) = exp(x*F(x)) where F(x) is the e.g.f. of A007106.

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.

E.g.f. satisfies: A(x/cosh(x)) = exp(x*tanh(x)). [From Paul D. Hanna, Aug 29 2008]