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Search: id:A143598
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| A143598 |
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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. |
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+0
1
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| 1, 2, 28, 1176, 103440, 15726880, 3684098496, 1232799974784, 558670427013376, 329559835063067136, 245462725323910487040, 225319148634038399801344, 249936012383478860884217856, 329609037187846742271984869376
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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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 (pauldhanna(AT)juno.com), Aug 29 2008]
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EXAMPLE
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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! +...
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A058014, A143600, A143601, A007106.
Sequence in context: A026944 A113633 A009674 this_sequence A071220 A063794 A168554
Adjacent sequences: A143595 A143596 A143597 this_sequence A143599 A143600 A143601
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2008
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