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A218301 E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(3*x)*cosh(3*x). 10
1, 3, 24, 252, 3360, 55008, 1074816, 24499968, 639744000, 18856765440, 619897847808, 22502300590080, 894419152404480, 38651030120693760, 1804765006764441600, 90574514900736933888, 4862862027933962207232, 278158492957848901779456, 16889663645642083220324352 (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*(n+3)^(n-1) * cosh((n+3)*x) * x^n/n!.
EXAMPLE
E.g.f.: A(x) = 1 + 3*x + 24*x^2/2! + 252*x^3/3! + 3360*x^4/4! + 55008*x^5/5! +...
where
A(x) = cosh(3*x) + 3*4^0*cosh(4*x)*x + 3*5^1*cosh(5*x)*x^2/2! + 3*6^2*cosh(6*x)*x^3/3! + 3*7^3*cosh(7*x)*x^4/4! + 3*8^4*cosh(8*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(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*(k+3)^(k-1)*cosh((k+3)*X)*x^k/k!); n!*polcoeff(Egf, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
Sequence in context: A080523 A203423 A319754 * A233833 A219536 A194957
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 25 2012
STATUS
approved

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Last modified April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)