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A002678
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Numerators of the Taylor coefficients of (e^x-1)^2.
(Formerly M4321 N1810)
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2
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1, 1, 7, 1, 31, 1, 127, 17, 73, 31, 2047, 1, 8191, 5461, 4681, 257, 131071, 73, 524287, 1271, 42799, 60787, 8388607, 241, 33554431, 22369621, 19173961, 617093, 536870911, 49981, 2147483647, 16843009, 53353631, 5726623061, 1108378657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| In 1929, Phillip Morse showed that a potential energy function of the form (e^x-1)^2 leads to a soluble Schroedinger equation. The numerators of its Taylor coefficients contain the Mersenne primes greater than 3. - David Broadhurst (D.Broadhurst(AT)open.ac.uk), Jan 19 2006
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REFERENCES
| H. E. Salzer, Tables of coefficients for differences in terms of their derivatives, Journal of Mathematics and Physics, 23 (1944), 210-212.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=2..300
Index entries for sequences related to Bernoulli numbers.
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FORMULA
| a(n) is the numerator of (2^n-2)/n! with generating function (e^x-1)^2 - David Broadhurst (D.Broadhurst(AT)open.ac.uk), Jan 19 2006
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MATHEMATICA
| Table[Numerator[Coefficient[Series[(E^x - 1)^2, {x, 0, 60}], x^n]], {n, 2, 60}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 04 2006
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PROG
| (PARI) print(vector(30, n, numerator((2^n-2)/n!))) (Broadhurst)
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CROSSREFS
| Cf. A002679.
Sequence in context: A146996 A083994 A084181 * A147482 A171770 A050402
Adjacent sequences: A002675 A002676 A002677 * A002679 A002680 A002681
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Jan 19 2006
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 04 2006
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