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 A136559 G.f.: A(x) = Sum_{n>=0} arctanh( 2^(2n+1)*x )^(2n+1) / (2n+1)!; a power series in x with integer coefficients. 3
 2, 0, 88, 0, 285088, 0, 112173964160, 0, 6667221644498203136, 0, 66605167708510907980664608768, 0, 120169056821375322042225614651624227643392, 0, 41233460218449924405779202537032142206549563511026450432, 0, 2796406262888046560966728498782777223041570797904775508376399120263413760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 2^n divides a(n) for n >= 0. LINKS G. C. Greubel, Table of n, a(n) for n = 1..49 EXAMPLE G.f.: A(x) = 2*x + 88*x^3 + 285088*x^5 + 112173964160*x^7 + ... MATHEMATICA Rest@With[{m=30}, CoefficientList[Series[Sum[ArcTanh[2^(2*j+1)*x]^(2*j+1)/(2*j + 1)!, {j, 0, m+2}], {x, 0, m}], x]] (* G. C. Greubel, Mar 15 2021 *) PROG (PARI) {a(n)=polcoeff(sum(k=0, n\2, atanh(2^(2*k+1)*x +x*O(x^n))^(2*k+1)/(2*k+1)!), n)} (Magma) m:=30; R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (&+[Argtanh(2^(2*j+1)*x)^(2*j+1)/Factorial(2*j+1): j in [0..m+2]]) )); // G. C. Greubel, Mar 15 2021 CROSSREFS Cf. A136558. Sequence in context: A136558 A156490 A216678 * A009740 A132860 A156485 Adjacent sequences: A136556 A136557 A136558 * A136560 A136561 A136562 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 10 2008 STATUS approved

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Last modified September 25 21:56 EDT 2023. Contains 365649 sequences. (Running on oeis4.)