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A168402
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E.g.f.: Sum_{n>=0} tanh(2^n*x)^n/n!.
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4
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1, 2, 16, 496, 63488, 32899584, 68048945152, 560546063546368, 18415227534711980032, 2416302301874471529480192, 1267360472364492854214927581184, 2658246833130441862918267501949222912
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [x^n/n! ] exp(2^n*tanh(x)).
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EXAMPLE
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E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 496*x^3/3! + 63488*x^4/4! +...
A(x) = 1 + tanh(2*x) + tanh(4*x)^2/2! + tanh(8*x)^3/3! + tanh(16*x)^4/4! +...+ tanh(2^n*x)^n/n! +...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(tanh(x)):
G(x) = 1 + x + x^2/2! - x^3/3! - 7*x^4/4! - 3*x^5/5! + 97*x^6/6! + 275*x^7/7! +...+ A003723(n)*x^n/n! +...
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MATHEMATICA
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nmax = 15; CoefficientList[Series[Sum[Tanh[2^k*x]^k/k!, {k, 0, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 11 2020 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(sum(k=0, n, tanh(2^k*x +x*O(x^n))^k/k!), n)}
(PARI) {a(n)=n!*polcoeff(exp(2^n*tanh(x +x*O(x^n))), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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