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A370456
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a(0) = 1, a(n) = (1/2) * Sum_{j=1..n} (1-(-1)^j-(-2)^j) * binomial(n,j) * a(n-j) for n > 0.
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2
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1, 2, 6, 29, 192, 1577, 15516, 178229, 2339952, 34559057, 567117876, 10237161629, 201592448712, 4300618438937, 98803485774636, 2432074390036229, 63857242954421472, 1781444969999245217, 52620896463516221796, 1640684857196257578029, 53847865360369426418232
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: 2*exp(2*x)/(1 + exp(x) + exp(2*x) - exp(3*x)).
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PROG
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(SageMath)
def a(m):
if m==0:
return 1
else:
return 1/2*sum([(1-(-2)^j-(-1)^j)*binomial(m, j)*a(m-j) for j in [1, .., m]])
list(a(m) for m in [0, .., 20])
(PARI) seq(n)={my(p=exp(x + O(x*x^n))); Vec(serlaplace(2*p^2/(1 + p + p^2 - p^3)))} \\ Andrew Howroyd, Feb 23 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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