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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
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
Sequence in context: A276361 A360973 A359972 * A242005 A276356 A012003
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 25 2012
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)