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Search: id:A141368
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| A141368 |
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G.f.: Sum_{n>=0} atanh(4^n*x)^n/n!, a power series in x having only integer coefficients. |
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+0
2
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| 1, 4, 128, 43712, 178978816, 9382678180864, 6558857974821945344, 62879510456046477909016576, 8439543050458648574249946721550336, 16110026905906831711301708576024644666261504
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = [x^n] [ sqrt((1+x)/(1-x)) ]^(4^n).
More generally, the following coefficient of x^n in the series:
[x^n] Sum_{n>=0} atanh(q^n*x)^n/n! = [x^n] [ sqrt((1+x)/(1-x)) ]^(q^n) is an integer for any even integer q.
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EXAMPLE
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G.f. A(x) = 1 + 4*x + 128*x^2 + 43712*x^3 + 178978816*x^4 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(sum(k=0, n, atanh(4^k*x +x*O(x^n))^k/k!), n)}
(PARI) {a(n)=polcoeff(((1+x)/(1-x +x*O(x^n)))^(4^n/2), n)}
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CROSSREFS
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Cf. A136749, A141367.
Sequence in context: A130318 A000318 A141367 this_sequence A057134 A041495 A117897
Adjacent sequences: A141365 A141366 A141367 this_sequence A141369 A141370 A141371
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 02 2008
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