A343580 a(n) = abs(A021009(n, floor(n/2))).

1, 1, 4, 18, 72, 600, 2400, 29400, 117600, 1905120, 7620480, 153679680, 614718720, 14841066240, 59364264960, 1669619952000, 6678479808000, 214453407168000, 857813628672000, 30967071995059200, 123868287980236800, 4965992272662220800, 19863969090648883200

Offset: 0

Author

Peter Luschny, Apr 20 2021

Keywords

• nonn

Comments

Absolute value of the middle coefficient of the Laguerre polynomials.

Links

• Wikipedia, Laguerre polynomials

Crossrefs

Cf. A021009, A295383.

Programs

Mathematica

a[n_] := Abs[Hypergeometric2F1[-Floor[n/2], n+1, 1, 1] n!/Floor[n/2]!];
Table[a[n], {n, 0, 20}]

PARI

a(n) = abs(n!*polcoef(pollaguerre(n), n\2)); \\ Michel Marcus, Apr 21 2021

SageMath

def a(n): return binomial(n, n - n//2)*falling_factorial(n, n - n//2)
print([a(n) for n in range(23)])

Formula

a(n) = ((-1)^floor(n/2)*n!/floor(n/2)!)*hypergeom([n + 1, -floor(n/2)], [1], 1).

a(n) = binomial(n, floor(n/2))*FallingFactorial(n, n - floor(n/2)).