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 A141368 G.f.: Sum_{n>=0} arctanh(4^n*x)^n/n!, a power series in x having only integer coefficients. 2
 1, 4, 128, 43712, 178978816, 9382678180864, 6558857974821945344, 62879510456046477909016576, 8439543050458648574249946721550336, 16110026905906831711301708576024644666261504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..40 FORMULA 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} arctanh(q^n*x)^n/n! = [x^n] [ sqrt((1+x)/(1-x)) ]^(q^n) is an integer for any even integer q. EXAMPLE G.f. A(x) = 1 + 4*x + 128*x^2 + 43712*x^3 + 178978816*x^4 + ... MATHEMATICA Table[SeriesCoefficient[(Sqrt[(1 + x)/(1 - x)])^(4^n), {x, 0, n}], {n, 0, 25}] (* G. C. Greubel, Apr 15 2017 *) PROG (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)} CROSSREFS Cf. A136749, A141367. Sequence in context: A000318 A229385 A141367 * A146555 A305568 A057134 Adjacent sequences:  A141365 A141366 A141367 * A141369 A141370 A141371 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 02 2008 STATUS approved

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Last modified April 23 00:56 EDT 2021. Contains 343197 sequences. (Running on oeis4.)