OFFSET
0,3
FORMULA
a(n) = factorial(ceiling(n/2))*fallfac(ceiling(n/2)+1, floor(n/2)), with fallfac = A008279.
D-finite with recurrence: (4*(n-2)^2 + 24*n - 80)*a(n) + (16*n+24)*a(n-1) - (n+2)*n*((n-2)^2 + 8*n - 17)*a(n-2) = 0. - Georg Fischer, Nov 23 2022
MAPLE
a:= n-> (m-> m!^2*(m+1))(iquo(n+1, 2, 'r'))/(2-r):
seq(a(n), n=0..24); # Alois P. Heinz, Feb 14 2024
PROG
(PARI) T(n, k) = n!/(n-k)!; \\ A008279
a(n) = ceil(n/2)!*T(ceil(n/2)+1, n\2); \\ Michel Marcus, Nov 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ran Pan, May 23 2015
STATUS
approved