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A218308 E.g.f. A(x) satisfies: A( x/(exp(4*x)*cosh(4*x)) ) = exp(3*x)*cosh(3*x). 10
1, 3, 42, 1116, 44616, 2394288, 161719200, 13187258304, 1261037553792, 138415816348416, 17155627044653568, 2370099000682257408, 361171910376568571904, 60185513513709805350912, 10887989148395358662270976, 2125192867898778619536457728 (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..15.

FORMULA

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

EXAMPLE

E.g.f.: A(x) = 1 + 3*x + 42*x^2/2! + 1116*x^3/3! + 44616*x^4/4! + 2394288*x^5/5! +...

where

A(x) = cosh(3*x) + 3*7^0*cosh(7*x)*x + 3*11^1*cosh(11*x)*x^2/2! + 3*15^2*cosh(15*x)*x^3/3! + 3*19^3*cosh(19*x)*x^4/4! + 3*23^4*cosh(23*x)*x^5/5! +...

PROG

(PARI) {a(n)=local(Egf=1, X=x+x*O(x^n), R=serreverse(x/(exp(4*X)*cosh(4*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*(4*k+3)^(k-1)*cosh((4*k+3)*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, A218309, A218310.

Sequence in context: A157542 A078601 A268621 * A195010 A333323 A331705

Adjacent sequences:  A218305 A218306 A218307 * A218309 A218310 A218311

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 25 2012

STATUS

approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)