A218306 E.g.f. A(x) satisfies: A( x/(exp(3*x)*cosh(3*x)) ) = exp(2*x)*cosh(2*x).

1, 2, 20, 392, 11648, 466112, 23517824, 1434077696, 102618951680, 8432793964544, 782753794531328, 81007725700038656, 9249066952457584640, 1154952975718091325440, 156588371428134115868672, 22908199202756436344963072, 3597006040171205977538822144

Offset

0,2

Comments

More generally, if A( x/(exp(t*x)*cosh(t*x)) ) = exp(m*x)*cosh(m*x), then A(x) = Sum_{n>=0} m*(n*t+m)^(n-1) * cosh((n*t+m)*x) * x^n/n!.

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: A(x) = Sum_{n>=0} 2*(3*n+2)^(n-1) * cosh((3*n+2)*x) * x^n/n!.

Example

E.g.f.: A(x) = 1 + 2*x + 20*x^2/2! + 392*x^3/3! + 11648*x^4/4! + 466112*x^5/5! +...
where
A(x) = cosh(2*x) + 2*5^0*cosh(5*x)*x + 2*8^1*cosh(8*x)*x^2/2! + 2*11^2*cosh(11*x)*x^3/3! + 2*14^3*cosh(14*x)*x^4/4! + 2*17^4*cosh(17*x)*x^5/5! +...

Prog

(PARI) {a(n)=local(Egf=1, X=x+x*O(x^n), R=serreverse(x/(exp(3*X)*cosh(3*X)))); Egf=exp(2*R)*cosh(2*R); n!*polcoeff(Egf, n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) /* Formula derived from a LambertW identity: */
{a(n)=local(Egf=1, X=x+x*O(x^n)); Egf=sum(k=0, n, 2*(3*k+2)^(k-1)*cosh((3*k+2)*X)*x^k/k!); n!*polcoeff(Egf, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A201595, A218300, A218301, A218302, A218303, A218304, A218305, A218307, A218308, A218309, A218310.

Sequence in context: A084948 A187661 A263207 * A009236 A078698 A090728

Adjacent sequences: A218303 A218304 A218305 * A218307 A218308 A218309

Keyword

nonn

Author

Paul D. Hanna, Oct 25 2012

Status

approved