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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 Table of n, a(n) for n=0..18. 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 Cf. A201595, A218300, A218302, A218303, A218304, A218305, A218306, A218307, A218308, A218309, A218310. Sequence in context: A080523 A203423 A319754 * A233833 A219536 A194957 Adjacent sequences: A218298 A218299 A218300 * A218302 A218303 A218304 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.)