A375077 Smallest k such that Product_{i=0..n} (k-i) divides C(2k,k).

2, 2480, 8178, 45153, 3648841

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Thomas Bloom, Problem 396

Prog

(PARI) for(n=1, 20, for(k=n+1, 100000, if(binomial(2*k, k)%prod(i=0, n, k-i)==0, print(n, " ", k); break)))
(Python)
from math import prod, comb
def A375077(n):
    a, c, k = prod(n+1-i for i in range(n+1)), comb(n+1<<1, n+1), n+1
    while c%a:
        k += 1
        a = a*k//(k-n-1)
        c = c*((k<<1)-1<<1)//k
    return k # Chai Wah Wu, Jul 30 2024

Crossrefs

Cf. A000984.

Sequence in context: A276650 A135234 A274962 * A199948 A261382 A281692

Adjacent sequences: A375074 A375075 A375076 * A375078 A375079 A375080

Keyword

nonn,hard,more

Author

Ralf Stephan, Jul 29 2024

Extensions

a(5) from Chai Wah Wu, Aug 01 2024

Status

approved