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 A174491 Denominator in the coefficient of x^n in exp( Sum_{m>=1} x^m/(m*2^(m^2)) ). 1
 1, 2, 32, 512, 262144, 33554432, 137438953472, 562949953421312, 147573952589676412928, 2417851639229258349412352, 2535301200456458802993406410752, 2658455991569831745807614120560689152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It is surprising that these terms should consist only of powers of 2. LINKS FORMULA a(n) = 2^(n^2)*A006519(n) where A006519(n) = highest power of 2 dividing n [conjecture]. EXAMPLE G(x) = exp( x/2 + x^2/(2*2^4) + x^3/(3*2^9) + x^4/(4*2^16) +...) G(x) = 1 + 1/2*x + 5/32*x^2 + 19/512*x^3 + 1921/262144*x^4 +... MATHEMATICA Table[Denominator@ SeriesCoefficient[Exp[Sum[x^m/(m*2^(m^2)), {m, 1, n}]], {x, 0, n}], {n, 0, 11}] (* Michael De Vlieger, May 12 2017 *) PROG (PARI) {a(n) = denominator(polcoeff(exp(sum(m=1, n+1, x^m/(m*2^(m^2))) + x*O(x^n)), n))} CROSSREFS Cf. A174490 (numerators). Sequence in context: A246213 A022028 A013776 * A022019 A010045 A052151 Adjacent sequences:  A174488 A174489 A174490 * A174492 A174493 A174494 KEYWORD frac,nonn AUTHOR Paul D. Hanna, Mar 25 2010 EXTENSIONS Edited by Paul D. Hanna, Mar 29 2010 STATUS approved

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Last modified January 26 06:41 EST 2022. Contains 350572 sequences. (Running on oeis4.)