OFFSET
1,1
COMMENTS
When n = k^2+3*k+1 is in A028387, C(n+k+3,n) = C(n+1,n) * C(n+k+1,n), so 0 != a(n) <= C(n+k+3,n). It appears that equality holds (verified for 0 <= k <= 100). In particular, a(11) = C(16,11) = 4368, a(19) = C(25,19) = 177100, a(29) = C(36,29) = 8347680, a(41) = C(49,41) = 450978066, ... .
a(34) = 4923689695575 = C(50,34) = C(35,34)*C(47,34).
a(6) > 10^29 (unless a(6) = 0). - Pontus von Brömssen, Jul 14 2024
EXAMPLE
a(1) = 4 = C( 4, 1) = C(2,1) * C(2,1).
a(2) = 36 = C( 9, 2) = C(4,2)^2.
a(3) = 560 = C(16, 3) = C(5,3) * C(8,3). (Also, C(16,3) = C(4,3)^2 * C(7,3)).
a(4) = 20475 = C(28, 4) = C(6,4) * C(15,4).
a(5) = 126 = C( 9, 5) = C(6,5) * C(7,5).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Jul 15 2023
STATUS
approved