OFFSET
2,3
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, Jan 19 2006
The integral f(z) = int((exp(z*exp(-y^2))-1)^2, {y, -infinity, infinity}) can be computed as sum(sqrt(Pi/k)*A002678(k)*(z^k/A002679(k)), {k, 1, infinity}). - Jean-François Alcover, Apr 03 2014
Also numerator of 2*Stirling2(n,2)/n!. - N. J. A. Sloane, Feb 14 2019
REFERENCES
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).
LINKS
T. D. Noe, Table of n, a(n) for n=2..300
H. E. Salzer, Tables of coefficients for differences in terms of the derivatives, Journal of Mathematics and Physics, 23 (1944), 210-212. See Table, row m=2.
FORMULA
a(n) is the numerator of (2^n-2)/n! with generating function (e^x-1)^2. - David Broadhurst, Jan 19 2006
MATHEMATICA
Table[Numerator[Coefficient[Series[(E^x - 1)^2, {x, 0, 60}], x^n]], {n, 2, 60}] (* Stefan Steinerberger, Apr 04 2006 *)
PROG
(PARI) print(vector(30, n, numerator((2^n-2)/n!))) \\ David Broadhurst, Jan 19 2006
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from David Broadhurst, Jan 19 2006
More terms from Stefan Steinerberger, Apr 04 2006
STATUS
approved