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A344398
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a(n) = (-1)^n * F_{n}((-1)^n * n), where F_{n}(x) is the Fubini polynomial.
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0
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1, 1, 10, 111, 8676, 243005, 49729758, 2634606331, 1026912225160, 88276603008249, 55954905981282210, 7103694104486331671, 6655958151527584785900, 1171100778886715057133493, 1521436331153097968932487206, 354408430829377435361459172915, 609729139653483641913607434550800
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OFFSET
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0,3
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LINKS
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MAPLE
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F := proc(n) option remember; if n = 0 then return 1 fi;
expand(add(binomial(n, k)*F(n-k)*x, k = 1..n)) end:
a := n -> (-1)^n*subs(x = (-1)^n*n, F(n)):
seq(a(n), n = 0..17);
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PROG
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(SageMath)
@cached_function
def F(n):
R.<x> = PolynomialRing(ZZ)
if n == 0: return R(1)
return R(sum(binomial(n, k)*F(n - k)*x for k in (1..n)))
def a(n):
return (-1)^n*F(n).substitute(x = (-1)^n*n)
print([a(n) for n in range(17)])
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CROSSREFS
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The coefficients of the Fubini polynomials are A131689.
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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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