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A218302 E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(4*x)*cosh(4*x). 10
1, 4, 40, 496, 7488, 134784, 2836736, 68635648, 1881948160, 57777184768, 1965962575872, 73503311167488, 2997314388623360, 132455836580577280, 6308164435588415488, 322185156718017642496, 17571327124936467677184, 1019377026461494381903872 (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..17.

FORMULA

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

EXAMPLE

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

where

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! +...

PROG

(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)}

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, 4*(k+4)^(k-1)*cosh((k+4)*X)*x^k/k!); n!*polcoeff(Egf, n)}

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

CROSSREFS

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

Sequence in context: A235372 A034385 A249927 * A296100 A214553 A074637

Adjacent sequences:  A218299 A218300 A218301 * A218303 A218304 A218305

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 25 2012

STATUS

approved

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Last modified June 29 10:15 EDT 2022. Contains 354912 sequences. (Running on oeis4.)