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A168402 E.g.f.: Sum_{n>=0} tanh(2^n*x)^n/n!. 4
1, 2, 16, 496, 63488, 32899584, 68048945152, 560546063546368, 18415227534711980032, 2416302301874471529480192, 1267360472364492854214927581184, 2658246833130441862918267501949222912 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) = [x^n/n! ] exp(2^n*tanh(x)).

EXAMPLE

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! +...

PROG

(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)}

CROSSREFS

Cf. A003723 (exp(tanh x)), variant: A136632.

Sequence in context: A012458 A012171 A068472 * A168406 A140310 A168403

Adjacent sequences:  A168399 A168400 A168401 * A168403 A168404 A168405

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 25 2009

EXTENSIONS

Example corrected by Paul D. Hanna, Nov 25 2009

STATUS

approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)