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A344397 a(n) = Stirling2(n, floor(n/2)) * floor(n/2)!. 1
1, 0, 1, 1, 14, 30, 540, 1806, 40824, 186480, 5103000, 29607600, 953029440, 6711344640, 248619571200, 2060056318320, 86355926616960, 823172919528960, 38528927611574400, 415357755774998400, 21473732319740064000, 258323865658578720000, 14620825330739032204800 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
a(n) = [x^(floor(n/2)] F(n, x), the middle coefficient of the Fubini polynomial.
a(n) = Sum_{k=0..n/2} (-1)^k*binomial((2*n - 1)/4 + (-1)^n/4, k)*((2*n - 1)/4 + (-1)^n/4 - k)^n.
MAPLE
a := n -> add((-1)^k*binomial((2*n-1)/4 + (-1)^n/4, k)*((2*n-1)/4 + (-1)^n/4 - k)^n, k = 0..n/2):
# Alternative, via Fubini recurrence:
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 -> coeff(F(n), x, iquo(n, 2));
seq(a(n), n = 0..22);
MATHEMATICA
a[n_] := StirlingS2[n, Floor[n/2]] * Floor[n/2]!; Array[a, 23, 0] (* Amiram Eldar, May 22 2021 *)
PROG
(SageMath)
def a(n): return stirling_number2(n, n//2) * factorial(n//2)
print([a(n) for n in range(23)])
CROSSREFS
Sequence in context: A293391 A015222 A054103 * A161454 A367950 A156203
KEYWORD
nonn
AUTHOR
Peter Luschny, May 21 2021
STATUS
approved

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Last modified May 5 17:32 EDT 2024. Contains 372277 sequences. (Running on oeis4.)