A218310 E.g.f. A(x) satisfies: A( x/(exp(5*x)*cosh(5*x)) ) = exp(x)*cosh(x).

1, 1, 12, 364, 17248, 1118816, 92306432, 9251542784, 1091729307648, 148280571406336, 22785577791987712, 3908379504145178624, 740274425760340901888, 153456630172316832628736, 34557831428406144298647552, 8401098284435734877893033984

Offset

0,3

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..15.

Formula

E.g.f.: A(x) = Sum_{n>=0} (5*n+1)^(n-1) * cosh((5*n+1)*x) * x^n/n!.

Example

E.g.f.: A(x) = 1 + x + 12*x^2/2! + 364*x^3/3! + 17248*x^4/4! + 1118816*x^5/5! +...
where
A(x) = cosh(x) + 6^0*cosh(6*x)*x + 11^1*cosh(11*x)*x^2/2! + 16^2*cosh(16*x)*x^3/3! + 21^3*cosh(21*x)*x^4/4! + 26^4*cosh(26*x)*x^5/5! +...

Prog

(PARI) {a(n)=local(Egf=1, X=x+x*O(x^n), R=serreverse(x/(exp(5*X)*cosh(5*X)))); Egf=exp(R)*cosh(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, (5*k+1)^(k-1)*cosh((5*k+1)*X)*x^k/k!); n!*polcoeff(Egf, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A201595, A218300, A218301, A218302, A218303, A218304, A218305, A218306, A218307, A218308, A218309.

Sequence in context: A012632 A081791 A166183 * A268550 A235685 A024298

Adjacent sequences: A218307 A218308 A218309 * A218311 A218312 A218313

Keyword

nonn

Author

Paul D. Hanna, Oct 25 2012

Status

approved