OFFSET
0,3
FORMULA
Let K(n, x) = 2^(n/2)*(-1/x^2)^(-n/2)*KummerU(-n/2, 1/2, -1/(2*x^2)) denote the Kummer polynomials, defined in A359760.
a(n) = K(n, n) for n >= 1.
MAPLE
PROG
(Python)
from math import factorial, comb
def oddfactorial(n: int) -> int: return factorial(2 * n) // (2**n * factorial(n))
def a(n: int) -> int:
return sum(comb(n, j) * oddfactorial(j//2) * n**j for j in range(0, n+1, 2))
print([a(n) for n in range(19)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 12 2023
STATUS
approved