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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
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OFFSET
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2,3
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COMMENTS
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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, Jan 19 2006
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REFERENCES
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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
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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
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a(n) is the numerator of (2^n-2)/n! with generating function (e^x-1)^2 - David Broadhurst, Jan 19 2006
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MATHEMATICA
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Table[Numerator[Coefficient[Series[(E^x - 1)^2, {x, 0, 60}], x^n]], {n, 2, 60}] - Stefan Steinerberger, Apr 04 2006
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PROG
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(PARI) print(vector(30, n, numerator((2^n-2)/n!))) (Broadhurst)
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CROSSREFS
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Cf. A002679.
Sequence in context: A146996 A083994 A084181 * A147482 A171770 A050402
Adjacent sequences: A002675 A002676 A002677 * A002679 A002680 A002681
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from David Broadhurst, Jan 19 2006
More terms from Stefan Steinerberger, Apr 04 2006
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STATUS
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approved
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