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#!/usr/bin/env python
"""
Calculates the Sloane's A000055 integer sequence, i.e. the "Number of
trees with n unlabeled nodes."
You can also google for "The On-Line Encyclopedia of Integer Sequences"
and paste in the sequence returned by this script:
1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106
and it will show you the A000055
"""
from sympy import Symbol, Poly
def T(x):
return x + x**2 + 2*x**3 + 4*x**4 + 9*x**5 + 20*x**6 + 48 * x**7 + \
115*x**8 + 286*x**9 + 719*x**10
def A(x):
return 1 + T(x) - T(x)**2/2 + T(x**2)/2
def main():
x = Symbol("x")
s = Poly(A(x), x)
num = list(reversed(s.coeffs()))[:11]
print(s.as_expr())
print(num)
if __name__ == "__main__":
main()
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