login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218302 E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(4*x)*cosh(4*x). 10

%I #7 Oct 25 2012 17:45:13

%S 1,4,40,496,7488,134784,2836736,68635648,1881948160,57777184768,

%T 1965962575872,73503311167488,2997314388623360,132455836580577280,

%U 6308164435588415488,322185156718017642496,17571327124936467677184,1019377026461494381903872

%N E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(4*x)*cosh(4*x).

%C More generally, if A( x/(exp(t*x)*cosh(t*x)) ) = exp(m*x)*cosh(m*x),

%C then A(x) = Sum_{n>=0} m*(n*t+m)^(n-1) * cosh((n*t+m)*x) * x^n/n!.

%F E.g.f.: A(x) = Sum_{n>=0} 4*(n+4)^(n-1) * cosh((n+4)*x) * x^n/n!.

%e E.g.f.: A(x) = 1 + 4*x + 40*x^2/2! + 496*x^3/3! + 7488*x^4/4! +...

%e where

%e A(x) = cosh(4*x) + 4*5^0*cosh(5*x)*x + 4*6^1*cosh(6*x)*x^2/2! + 4*7^2*cosh(7*x)*x^3/3! + 4*8^3*cosh(8*x)*x^4/4! + 4*9^4*cosh(9*x)*x^5/5! +...

%o (PARI) {a(n)=local(Egf=1,X=x+x*O(x^n),R=serreverse(x/(exp(X)*cosh(X)))); Egf=exp(4*R)*cosh(4*R); n!*polcoeff(Egf,n)}

%o for(n=0,25,print1(a(n),", "))

%o (PARI) /* Formula derived from a LambertW identity: */

%o {a(n)=local(Egf=1,X=x+x*O(x^n)); Egf=sum(k=0,n,4*(k+4)^(k-1)*cosh((k+4)*X)*x^k/k!); n!*polcoeff(Egf,n)}

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A201595, A218300, A218301, A218303, A218304, A218305, A218306, A218307, A218308, A218309, A218310.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 25 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)