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URL: https://oeis.org/A388426

⇱ A388426 - OEIS

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A388426
Triangle of palindromic polynomials.
1
1, 1, 1, 1, 5, 1, 1, 16, 16, 1, 1, 43, 121, 43, 1, 1, 106, 666, 666, 106, 1, 1, 249, 3089, 6649, 3089, 249, 1, 1, 568, 12916, 51976, 51976, 12916, 568, 1, 1, 1271, 50481, 348471, 641281, 348471, 50481, 1271, 1, 1, 2806, 188398, 2106622, 6488230, 6488230, 2106622, 188398, 2806, 1
OFFSET
0,5
COMMENTS
This should be the h^* vectors of some reflexive polytopes.
FORMULA
E.g.f.: (s-1)/(s-exp((s-1)*x))*exp(s*x*(s-1)/(s-exp((s-1)*x))).
EXAMPLE
Triangle begins:
[1],
[1, 1],
[1, 5, 1],
[1, 16, 16, 1],
[1, 43, 121, 43, 1],
[1, 106, 666, 666, 106, 1]
...
PROG
(SageMath)
Bs = PolynomialRing(QQ, 's')
s = Bs.gen()
La = LazyPowerSeriesRing(Bs, 'u')
u = La.gen()
f = (s-1)/(s-exp((s-1)*u))*exp(s*u*(s-1)/(s-exp((s-1)*u)))
[list(f[n] * factorial(n)) for n in range(9)]
CROSSREFS
Row sums are A002720. Alternating row sums are A354020.
Similar to A046802.
Cf. A053221.
Sequence in context: A174159 A074060 A157637 * A157181 A347974 A029847
KEYWORD
nonn,tabl
AUTHOR
F. Chapoton, Oct 15 2025
STATUS
approved