A372904 Numbers k that divide the k-th central trinomial coefficient.

1, 21, 387, 657, 6291, 16113, 25767, 54243, 56457, 96141, 155601, 294273, 300871, 453781, 653421, 660879, 669609, 951881, 993307, 1246077, 1438623, 1535409, 1870533, 2110941, 2510109, 2959173, 2974239, 3158541, 3242673, 3569337, 4139739, 4789273, 5405643, 7034097

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn

Comments

Numbers k such that k | A002426(k).

Also, numbers k that divide the k-th Riordan number: k | A005043(k).

Apparently a subsequence of A266969.

Examples

			21 is a term since A002426(21) = 1105350729 = 21 * 52635749 is divisible by 21.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..38

Crossrefs

Cf. A002426, A005043.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Programs

Mathematica

Select[Range[1000], Divisible[4^#*JacobiP[#, -# - 1/2, -# - 1/2, -1/2], #] &]

PARI

lista(kmax) = {my(ct0 = 1, ct1 = 1, ct2); print1("1, "); for(k = 2, kmax, ct2 = ((2*k-1)*ct1 + 3*(k-1)*ct0)/k; if(!(ct2 % k), print1(k, ", ")); ct0 = ct1; ct1 = ct2);}