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A218304 E.g.f. A(x) satisfies: A( x/(exp(2*x)*cosh(2*x)) ) = exp(3*x)*cosh(3*x). 10
1, 3, 30, 468, 10248, 291888, 10282464, 432631104, 21195292800, 1186054914816, 74676568432128, 5226914768016384, 402722750814750720, 33876716756962652160, 3089713688099323502592, 303723970839738425622528, 32015024916407062538256384 (list; graph; refs; listen; history; text; internal format)
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} 3*(2*n+3)^(n-1) * cosh((2*n+3)*x) * x^n/n!.

EXAMPLE

E.g.f.: A(x) = 1 + 3*x + 30*x^2/2! + 468*x^3/3! + 10248*x^4/4! + 291888*x^5/5! +...

where

A(x) = cosh(3*x) + 3*5^0*cosh(5*x)*x + 3*7^1*cosh(7*x)*x^2/2! + 3*9^2*cosh(9*x)*x^3/3! + 3*11^3*cosh(11*x)*x^4/4! + 3*13^4*cosh(13*x)*x^5/5! +...

PROG

(PARI) {a(n)=local(Egf=1, X=x+x*O(x^n), R=serreverse(x/(exp(2*X)*cosh(2*X)))); Egf=exp(3*R)*cosh(3*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, 3*(2*k+3)^(k-1)*cosh((2*k+3)*X)*x^k/k!); n!*polcoeff(Egf, n)}

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

CROSSREFS

Cf. A201595, A218300, A218301, A218302, A218303, A218305, A218306, A218307, A218308, A218309, A218310.

Sequence in context: A294240 A007004 A276361 * A242005 A276356 A012003

Adjacent sequences:  A218301 A218302 A218303 * A218305 A218306 A218307

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 25 2012

STATUS

approved

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Last modified May 21 15:27 EDT 2019. Contains 323444 sequences. (Running on oeis4.)