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 A178449 Conjectured expansion of exp(Pi sqrt(163)) in powers of t, where t = 1/(640320)^3. 0
 1, 744, -196884, 167975456, -180592706130, 217940004309743, -19517553165954887, 74085136650518742, -131326907606533204 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 COMMENTS R. W. Gosper asks if the coefficients are well-defined. Until this is answered, the sequence is only conjectural. This series is very close to A178451, but presumably different from it. REFERENCES R. W. Gosper, Posting to the Math Fun Mailing List, Dec 21 2010 LINKS EXAMPLE e^(Pi sqrt(163)) = s^3 + 744 - 196884/s^3 + 167975456/s^6 - 180592706130/s^9 + 217940004309743/s^12 - 19517553165954887/s^15 + 74085136650518742/s^18 - ... where s = 640320. Now set t = 1/s^3. PROG /* GNU bc code, computes a(0) through a(7) */ define trunc(x) { auto sc, t; sc=scale; scale=0; t=x/1; scale=sc; return(t) } scale = 200; pi = 4 * a(1); r = e(pi * sqrt(163)); s = 640320; c0 =  1 + trunc(r - s^3); c1 = -1 - trunc(((s^3 + c0) - r) * s^3); c2 =  1 + trunc((r - (s^3 + c0 + c1/s^3)) * s^6); c3 = -1 - trunc(((s^3 + c0 + c1/s^3 + c2/s^6) - r) * s^9); c4 =  1 + trunc((r - (s^3 + c0 + c1/s^3 + c2/s^6 + c3/s^9)) * s^12); c5 = -1 - trunc(((s^3 + c0 + c1/s^3 + c2/s^6 + c3/s^9 + c4/s^12) - r) * s^15); c6 =  1 + trunc((r - (s^3 + c0 + c1/s^3 + c2/s^6 + c3/s^9 + c4/s^12 + c5/s^15)) * s^18); c7 = -1 - trunc(((s^3 + c0 + c1/s^3 + c2/s^6 + c3/s^9 + c4/s^12 + c5/s^15 + c6/s^18) - r) * s^21); CROSSREFS Cf. A000521, A091406, A178451, A066396. Sequence in context: A192731 A288261 A000521 * A178451 A066395 A161557 Adjacent sequences:  A178446 A178447 A178448 * A178450 A178451 A178452 KEYWORD sign AUTHOR N. J. A. Sloane, Dec 22 2010, based on a posting by R. W. Gosper to the Sequence Fans Mailing List, Dec 21 2010 EXTENSIONS Cullen link, bc code, and a(8) from Robert Munafo, Dec 23 2010 STATUS approved

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)